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Lesson in mathematics on the topic "Properties of logarithms"
Math lesson prepared by: Garina Elena Ivanovna, teacher of mathematics, Humanitarian Technical College, Orenburg, email: [email protected]
Goals:
- the formation of information competence through the ability to draw independent conclusions and generalizations, analyze and review the answers of comrades;
- formation of educational and cognitive competence in the course of developing self-control skills, identifying and highlighting significant parts of the whole;
- the formation of communicative competence in the course of active dialogues, the ability to substantiate judgments, to give definitions.
Lesson type: knowledge consolidation lesson.
Equipment: multimedia equipment, tables for oral counting.
During the classes
1.Org.moment
2.Updating knowledge. Checking previously acquired knowledge. Mutual verification.
Each of you has a “Checklist” on your desk. Let's try to check how you prepared for today's lesson. The title of this test is "Catch the Mistake!"
The check sheet contains the properties of logarithms with errors. Your task next to the erroneous version of the properties is to write them in the correct version.
The correct options are on the slide.
Get the error!
Now exchange checklists next to each correctly written property + , next to the wrong one - .
Submit checklists for scoring.
3. Setting goals and objectives of the lesson.
You are invited to choose from the proposals those that, in your opinion, could be attributed to the goals and objectives of the lesson.
Choose and continue the phrase: “Today in the lesson we ...”
- Solve exercises using the properties of logarithms.
- Solve text problems for movement.
- Simplify logarithmic expressions.
- Apply the definition of the logarithm when solving exercises.
- Solve tasks on your own using the properties and definition of logarithms.
4. Oral account. Warm up.
The objectives of the lesson are defined. To begin with, let's work orally, in order to move on to more complex tasks.
Calculate:
docmat69/docmat69.rar"> RAR 2.42 Mb
Methodical development of a lesson in mathematics
"Logarithms and their properties"
The purpose of the lesson:
educational- introduce the concept of a logarithm, study the basic properties of logarithms and contribute to the formation of the ability to apply the properties of logarithms when solving tasks.
Educational- develop mathematical thinking; calculation technique; the ability to think logically and work rationally; to promote the development of self-control skills in students.
Educational- to promote the education of interest in the topic, to cultivate a sense of self-control, responsibility.
Lesson objectives:
To develop in students the ability to compare, compare, analyze, draw independent conclusions.
Key competencies: the ability to independently search, extract, systematize, analyze and select information necessary for solving educational problems; the ability to independently master the knowledge and skills necessary to solve the problem.
Lesson type: A lesson in the study and primary consolidation of new knowledge.
Equipment: computer, multimedia projector, presentation "Logarithms and their properties", handouts.
Keywords: logarithm; properties of the logarithm.
Software: MS power point.
Intersubject communications: story.
Intra-subject communications: "The root of the n-th degree and their properties".
Lesson Plan
Organizing time.
Repetition of the material covered.
Explanation of new material.
Consolidation.
Independent work.
Homework. Summing up the lesson.
During the classes:
- Organizing moment: checking the readiness of students for the lesson; officer's report .
Good afternoon students.
I want to start this lesson with the words of A.N. Krylova: “Sooner or later, every correct mathematical idea finds application in this or that matter.”
Repetition of the material covered.
Students are asked to remember:
What is degree, base and exponent.
nth root of a number a a number is called whose nth power is equal to a. 3 4 = 81.
2) Basic properties of degrees.
3. Post a new topic.
Now let's move on to a new topic. The topic of today's lesson is the Logarithm and its properties (open notebooks and write down the date and topic).
In this lesson, we will get acquainted with the concept of "logarithm", we will also consider the properties of logarithms. This topic is relevant, because. the logarithm is always found on the final certification in mathematics.
Let's ask a question:
1) To what power must 3 be raised to get 9? Obviously the second. The exponent to which you need to raise the number 3 to get 9 is 2.
2) To what power must 2 be raised to get 8? Obviously the second. The exponent to which you need to raise the number 2 to get 8 is 3.
In all cases, we were looking for an indicator of the degree to which something needs to be raised in order to get something. The exponent to which something needs to be raised is called a logarithm and is denoted by log.
The number that we raise to a power, i.e. the base of the degree is called the base of the logarithm and is written in a subscript. Then the number that we receive is written, i.e. the number we are looking for: log 3 9=2
This entry reads: "Logarithm of the number 9 to base 3." The base 3 logarithm of 9 is the exponent to which you need to raise 3 to get 9. This exponent is 2.
Likewise the second example.
We give the definition of the logarithm.
Definition. The logarithm of a number b>0 by reason a>0, a ≠ 1 is the exponent to which the number must be raiseda, to get a numberb .
The logarithm of a number b by reason a denoted log a b.
History of the logarithm:
Logarithms were introduced by the Scottish mathematician John Napier (1550-1617) and the mathematician Jost Burgi (1552-1632).
From the point of view of computational practice, the invention of logarithms, if possible, can be safely placed side by side with other, more ancient, great inventions of the Hindus - our decimal numbering system.
A dozen years after the appearance of Napier's logarithms, the English scientist Gunter invented a very popular counting device - a slide rule.
She helped astronomers and engineers in their calculations, she made it possible to quickly get an answer with sufficient accuracy of three significant figures. Now calculators have supplanted it, but without the slide rule, neither the first computers nor microcalculators would have been built.
Consider examples:
log 3 27=3; log 5 25=2; log 25 5=1/2; log 5 1/125=-3; log -2 -8- does not exist; log 5 1=0; log 4 4=1
Consider these examples:
ten . log a 1=0, a>0, a ≠ 1;
twenty . log a a=1, a>0, a ≠ 1.
These two formulas are properties of the logarithm. Write down the properties and they need to be remembered.
In mathematics, the following abbreviation is accepted:
log 10 a=lga is the decimal logarithm of the number a(the letter "o" is skipped, and the base 10 is not put).
log e a=lna - natural logarithm of a."e" is such an irrational number equal to 2.7 (the letter “o” is omitted, and the base “e” is not put).
Consider examples:
log 10=1; log 1=0
log e=1 ; log 1=0 .
How to go from logarithmic to exponential: log a b\u003d s, s - is the logarithm, the exponent to which you want to raise a, To obtain b. Consequently, a degree With equals b: a With = b.
Consider five logarithmic equalities. Task: to check their correctness. These examples contain errors. Let's use this diagram to test it.
lg 1 = 2 (10 2 =100)- this equation is not correct.
log 1/2 4 = 2- this equation is not correct.
log 3 1=1 - this equation is not correct.
log 1/3 9 = -2 - this equality is correct.
log 4 16 = -2- this equation is not correct.
We derive the main logarithmic identity: a log a b = b
Consider an example.
5 log 5 13 =13
Properties of logarithms:
3°. log a xy = log a x + log a y.
4°. log a x/y = log a x - log a y.
5°. log a x p = p · log a x, for any real p.
Consider an example for checking 3 properties:
log 2 8 + log 2 32= log 2 8∙32= log 2 256=8
Consider an example for checking 5 properties:
3∙ log 2 8= log 2 8 3 = log 2 512 =9
3∙3 = 9
The formula for going from one base of a logarithm to another base is:
This formula will be required when calculating the logarithm using a calculator. Let's take an example: log 3 7 = lg7 / lg3. The calculator can only calculate the decimal and natural logarithm. Enter the number 7 and press the "log" button, also enter the number 3 and press the "log" button, divide the upper value by the lower and get the answer.
- Consolidation.
- log 6 6
Here are 8 solved examples, among which there are correct ones, the rest with an error. Determine the correct equality (name its number), correct the errors in the rest.
- log 2 32+ log 2 2= log 2 64=6
log 5 5 3 = 2;
log 3 45 - log 3 5 = log 3 40
3∙log 2 4 = log 2 (4∙3)
log 3 15 + log 3 3 = log 3 45;
2∙log 5 6 = log 5 12
3∙log 2 3 = log 2 27
log 2 16 2 = 8.
- Checking ZUN - independent work on cards.
- log 4 16 log 25 125 log 8 2 log 6 6
- log 3 27 log 4 8 log 49 7 log 5 5
Summarizing. Homework. Grading.
Lesson on the topic "Logarithm, its properties."
Chertikhina L.P.
teacher
GB POU "VPT"
"Take as much as you can and want,
but not less than mandatory.
Lesson Objectives:
know and be able to write down the definition of the logarithm, the basic logarithmic identity;
be able to apply the definition of the logarithm and the basic logarithmic identity when solving exercises;
get acquainted with the properties of logarithms;
learn to distinguish the properties of logarithms by their recording;
learn how to apply the properties of logarithms when solving tasks;
consolidate computing skills;
continue to work on mathematical speech.
to form skills of independent work, work with a textbook, skills of independent acquisition of knowledge;
develop the ability to highlight the main thing when working with text;
to form the independence of thinking, mental operations: comparison, analysis, synthesis, generalization, analogy;
show students the role of systematic work to deepen and improve the strength of knowledge, the culture of completing tasks;
develop students' creativity.
Lesson type: communication of new knowledge.
Time spending: 1,5 hour
Equipment:
log property table
task cards;
Teacher's PC, multimedia projector;
Lesson PlanOrganizing time. 1 minute.
Goal setting. 1 minute.
Checking previously learned material 5 min
Introduction to the concept of logarithm.
Definition of a logarithm. 5 minutes
6.Historical background 10 min
Basic logarithmic identity. 10 min
Basic properties of logarithms 10 min
Generalization and systematization of knowledge. 7 min.
Homework. 1 minute.
Creative application of knowledge, skills and abilities. 25 min.
Summarizing. 5 minutes.
Guys, today in the lesson you have to test the ability to solve the simplest exponential equations so that you can introduce a new concept for you, then we will get acquainted with the properties of the new concept; you must learn to distinguish these properties by writing them; learn how to apply these properties in solving problems.
Be collected, attentive and observant. Good luck!
Checking previously studied material.Students are invited to determine the topic of the lesson by solving equations
2 x =; 3 x =; 5 x \u003d 1/125; 2 x \u003d 1 / 4;
2 x = 4; 3 x = 81; 7 x \u003d 1 / 7; 3 x = 1/81
- Name the new concept that we will get acquainted with:
- The topic of our lesson is “Logarithm and its properties”. Try to find the root of the equation 2 x = 5. We can write the answer to this equation using a new concept. Read the text of the slide and write down the root of the equation.
4.1. Definition of logarithm(slides 5-7)The logarithm of a positive number b to the base a, where a0, a ≠ 1, is the exponent to which a must be raised to get the number b.
1) log 10 100 = 2, because 10 2 \u003d 100 (definition of the logarithm and properties of the degree),
2) log 5 5 3 = 3, because 5 3 = 5 3 (…),
3) log 4 = –1, because 4 -1 = (...).
In recording b=at number a is the base of the degree, t- indicator, b- degree. Number t -is the exponent to which the base a must be raised to obtain the number b. Consequently, t is the logarithm of the number b by reason a: t=log
a
b
.
Substituting in equality t=logab expression b in the form of a degree, we get one more identity:
log a a t =t .
We can say that the formulas at=b and t=logab are equivalent, they express the same relationship between numbers a, b and t(at a0, a1, b0). Number t- arbitrarily, no restrictions are imposed on the exponent.
Substituting into equality at=b number entry t in the form of a logarithm, we get an equality called basic logarithmic identity
:
=b
.
1) (3 2) log 3 7 = (3 log 3 7) 2 = 7 2 = 49 (power of degree, basic logarithmic identity, definition of degree),
2) 7 2 log 7 3 = (7 log 7 3) 2 = 3 2 = 9 (…),
3) 10 3 log 10 5 = (10 log 10 5) 3 = 5 3 = 125 (…),
4) 0.1 2 log 0.1 10 = (0.1 log 0.1 10) 2 = 10 2 = 100 (…).
You did a great job with the examples. Now calculate the following tasks written on the board:
a) log 15 3 + log 15 5 = ...,
b) log 15 45 – log 15 3 = …,
c) log 4 8 =…,
d) 7 = ... .
What do you think we need to know in order to perform operations with logarithms?
If students have difficulties, then ask the question: “In order to perform actions with degrees, what do you need to know?” (Answer: “Properties of degree”). Revisit the original question. (Properties of logarithms)
Here is a table with the properties of logarithms. It is necessary to give a name to each property and correctly formulate them.
| The name of the property of logarithms | Properties of logarithms |
|
| unit logarithm. | log a 1 = 0, a 0, a 1. |
|
| base logarithm. | log a a = 1, a 0, a 1. |
|
GBPOU "Rzhev College"
Outline of an open lesson
Subject: "Algebra and the beginnings of mathematical analysis"
in the 1st year group of GBPOU "Rzhev College"
on the topic "Properties of the logarithm"
Developed by: math teacherSergeeva T.A.
Rzhev, 2016
Lesson topic . Properties of the logarithm
Lesson type. Studying and consolidating new knowledge. Application of knowledge in practice
lesson technology.
Information and communication, development of research skills, a differentiated approach to teaching.
The purpose of the lesson .
To create conditions for the personal self-realization of each student in the process of studying the topic:« Properties of logarithms», promote the development of personal, educational, cognitive, communicative competencies.
Tasks.
Educational: Update students' knowledge on the topic "Properties of logarithms";Formation of skills to solve logarithmic expressions. Generalize and systematize the acquired knowledge on the topic "Logarithm".
Developing: To promote the development of mental operations in students: the ability to analyze, synthesize, compare;develop the skills of building a logical chain of reasoning;promote the development of independent problem solving, skills of mutual control and self-control; develop literate mathematical speech
Educational: Develop attention, independence when working in the classroom;Contribute to the formation of activity and perseverance, maximumworking capacity;Develop interest in mathematics lessons.
The choice of the content of educational material, methods, forms of work in the lesson: The main didactic method: problematic and partially search. Private methods and techniques: frontal and individual work
Planned educational outcomes.
Subject UUD: development of systematic knowledge, their transformation, application and independent replenishment, possession of ideas about logarithms and their properties.
Personal UUD: show attention and interest in the educational process, be able to analyze, assess the situation, evaluate their own learning activities, show independence, initiative, responsibility, compare different points of view, reckon with the opinion of another, be able to work in pairs and groups, argue their point of view.
Metasubject UUD:
Regulatory UUD: the ability to apply and save the learning task, plan the solution of the task, make changes to the process, outline ways to eliminate errors, and exercise final control.
Cognitive UUD : be able to search for and process information, write it down and perceive; use models, signs, symbols and schemes; carry out logical operations: analysis, synthesis, comparison, summing up the concept, analogy, judgment, choose ways to solve problems depending on specific conditions.
Communicative UUD: to form the ability to cooperate with a teacher and peers in solving a learning problem, to take responsibility for the result of their actions; develop the ability to listen and engage in dialogue; to form attentiveness and accuracy in calculations; to cultivate a sense of mutual assistance, a culture of educational work, a demanding attitude towards oneself and one's work.
Basic terms, concepts. Properties of a degree with a real exponent, definition of a logarithm, types of logarithms, basic logarithmic identity.
Equipment computer, multimedia projector, presentation "Logarithm", handout, study guideA.G. Mordkovich "Algebra 10-11".
Lesson Plan
1. Introductory - motivational part . (1 min )
1.1. Organizing time.
1.2.
2. Main part lesson . (36 min )
2.1 15 minutes
2.2. 7 min
2.3. 7 min
2.4. 7 min
3. Reflective-evaluative part of the lesson. (8 min)
3.1. Homework. 1 minute
3.2. Independent work with self-test according to the standard. 6 min.
3.3. Reflection. 1 minute
During the classes
1. Introductory - motivational part .
1.1. Organizing time.
Mutual greeting; checking those present at the lesson according to the class journal, the preparedness of students for the lesson (workplace, appearance);
1.2. Motivation for learning activities.
- What branch of algebra are we studying? (Logarithms) (Slide 1)
- What do you already know about this section of algebra?
(Definition of the logarithm, basic logarithmic identity, properties of the logarithm, logarithmic function, plotting logarithmic functions (calculation and transformation of the logarithm)
- Define a logarithm. (Slide 2)
- What follows from the definition of the logarithm. (Basic logarithmic identity)
- Write down the basic logarithmic identity in your notebook.
- Before you is the "Evaluation sheet", fill it out by writing your full name and group. In the lesson, according to this sheet, your knowledge of this scheme will be assessed, and the results obtained are recorded in it.(Attachment 1). The grade for today's lesson will be calculated based on the received average score, which you will calculate yourself.
- In accordance with the criteria recorded in the "Evaluation Sheet", rate yourself for knowledge of the theoretical material.
2. Main part lesson .
2. 1. Independent activity according to a known norm and the organization of educational difficulties.
- You have repeated all the theoretical knowledge in this section, let's check it in practice
We count orally (Slide 3)
According to the criteria written in the "Score Sheet", rate yourself for correct calculations.
- Now we can apply this knowledge to solve tasks: Open workbooks and complete tasks from cards. (Slide 4 )
Independent work No. 1 ,
Option 1
1)
2) 
3)
4) 
5) 
6) 
7) 
8) 
9) 
Option 2
1)
2) 
3)
4) 
5) 
6) 
7) 
8) 
9) 
- Pass the notebook to your desk mate. Let's check the correctness of the solution. (Slide5 )
(Students compare their solutions in their notebooks and write down the correct answers)
Now say:
- What was used to solve the problem?
(Properties of powers. Definition of a logarithm. Basic logarithmic identity.)
What do you see as the difficulty of the solution?
What tasks did you fail to solve and what is the problem? (No. 8, 9)
What is the reason for the difficulty?
(Not enough knowledge)
- In accordance with the criteria written in the card, mark yourself as #1 for independent work.
2.2. Construction of the project of an exit from difficulty.
Now we need to analyze the tasks that caused you difficulties.
- What do we need to know to perform actions with logarithms?
(Properties of logarithms). (Slide6 )
- We work in groups (3 groups). One student works at the blackboard, the group helps to find the right solution.
1 group : Perform transformations
and 
, where 
and 
In our example, there is a “+” sign, according to the properties of the degrees, the exponents are added if the bases are the same and the action “multiplication”
Therefore
2 group : Perform transformations
When performing transformations of an expression containing logarithms, various properties are used.
What the basic logarithmic identity tells us
- Let's return to example 8 from independent work No. 1
We rewrite it using the basic logarithmic identity and get
and 
From the definition, we know that the logarithm is the exponent to which the base must be raised. to get a positive number , where 
and
In our example, there is a “-” sign, according to the properties of the degrees, the exponents are subtracted if the bases are the same and the action “division”
4. Implementation of the constructed project.
A positive result is not proof. Let us prove the obtained equalities.
Property 1 the teacher proves together with the students.
1 variant proves property 2.
2 variant proves property 3.
5. Primary consolidation of skills and abilities.
- Now let's try to solve examples (Work at the blackboard) (Slide 7)
The student decides at the blackboard the group helps
8. Reflection.
- For work in the lesson ...... get grades, put them in the "Evaluation sheet". Summarize and give a final grade. After checking your work in the “Score Sheet”, I will give you my final grade, taking into account the activity in the lesson, and in the next lesson we will compare them.
Acquaintance with the logarithm does not end, in the next lessons we will solve equations and inequalities. In conclusion, I want to recall the phrase of the French scientist (Slide 10) Laplace: “Logarithms have reduced calculations, lengthening our lives.”
I wish you that acquaintance with logarithms will help you in life, lengthening it and adding beauty to it.
Thank you all for the lesson.
"Take as much as you can and want,
but not less than mandatory.
Lesson Objectives:
- know and be able to write down the definition of the logarithm, the basic logarithmic identity;
- be able to apply the definition of the logarithm and the basic logarithmic identity when solving exercises;
- get acquainted with the properties of logarithms;
- learn to distinguish the properties of logarithms by their recording;
- learn how to apply the properties of logarithms when solving tasks;
- consolidate computing skills;
- continue to work on mathematical speech.
- to form skills of independent work, work with a textbook, skills of independent acquisition of knowledge;
- develop the ability to highlight the main thing when working with text;
- to form the independence of thinking, mental operations: comparison, analysis, synthesis, generalization, analogy;
- show students the role of systematic work to deepen and improve the strength of knowledge, the culture of completing tasks;
- develop students' creativity.
Basic knowledge:
- definition of an exponential function;
- properties of the exponential function;
- definition of an exponential equation, basic methods and techniques for solving exponential equations;
Lesson type: communication of new knowledge.
Working methods:
- problem;
- partially search.
Types of jobs:
- individual;
- collective;
- individual-collective;
- frontal.
Motivation for cognitive activity: in the classroom, it is necessary to provide students with the opportunity to show ingenuity, ingenuity in the formation of skills for independent work, work with a textbook, skills for independent acquisition of knowledge.
Time spending: 1,5 hour
Equipment:
- table of properties of logarithms;
- text "From the history of logarithms";
- posters;
- task cards;
- educational cards;
- test suite;
- signal clock;
- Teacher's PC, multimedia projector;
- Presentation, containing material for repeating and consolidating theoretical knowledge, for developing the skills of practical application of theory to solving exercises, creating a problem situation , for self-control, containing information from the history of logarithms
Lesson Plan
- Organizing time. 1 minute.
- Goal setting. 1 minute.
- Checking previously learned material 5 min
- Introduction to the concept of logarithm.
- Definition of a logarithm. 5 minutes
- Historical background 10 min
- Slide Rule 10 min
- Basic logarithmic identity. 10 min
- Basic properties of logarithms 10 min
- Generalization and systematization of knowledge. 7 min.
- Homework. 1 minute.
- Creative application of knowledge, skills and abilities. 25 min.
- Summarizing. 5 minutes.
During the classes:
1. Organizing time. Greetings.
2. Goal setting.
Guys, today in the lesson you have to test the ability to solve the simplest exponential equations so that you can introduce a new concept for you, then we will get acquainted with the properties of the new concept; you must learn to distinguish these properties by writing them; learn how to apply these properties in solving problems.
Be collected, attentive and observant. Good luck!
3. Verification of previously studied material.(slides 1-2)
Students are invited to determine the topic of the lesson by solving equations
2 x =; 3 x =; 5 x \u003d 1/125; 2 x \u003d 1 / 4;
2 x = 4; 3 x = 81; 7 x \u003d 1 / 7; 3 x = 1/81
- Name the new concept that we will get acquainted with:
| W | M | L | G | E | R | F | O | And | BUT |
| 5 | – 4 | 2/3 | – 3 | – 2/7 | 2 | – 1 | 1/2 | 4 | – 2 |
4. Introduction of the concept of logarithm.(slides 3,4)
- The topic of our lesson is “Logarithm, its properties”. Try to find the root of the equation 2 x = 5. We can write the answer to this equation using a new concept. Read the text of the slide and write down the root of the equation.
4.1. Definition of logarithm(slides 5-7)
The logarithm of a positive number b to the base a, where a>0, a ≠ 1, is the exponent to which a must be raised to get the number b.
1) log 10 100 = 2, because 10 2 \u003d 100 (definition of the logarithm and properties of the degree),
2) log 5 5 3 = 3, because 5 3 = 5 3 (…),
3) log 4 = –1, because 4 -1 = (...).
4.2. History reference(slides 8-11)
From the history of logarithms.
4.3. Slide rule
Ruler, the grandmother of the computer.
From the history of the logarithm
4.4. Basic logarithmic identity(slides 12-14)
In recording b=a t number a is the base of the degree, t- indicator, b- degree. Number t - is the exponent to which the base a must be raised to obtain the number b. Consequently, t is the logarithm of the number b by reason a: t=log a b.
Substituting in equality t=log a b expression b in the form of a degree, we get one more identity:
log a a t =t.
We can say that the formulas a t =b and t=log a b are equivalent, they express the same relationship between numbers a, b and t(at a>0, a1, b>0). Number t- arbitrarily, no restrictions are imposed on the exponent.
Substituting into equality a t =b number entry t in the form of a logarithm, we get an equality called basic logarithmic identity
:
=b.
1) (3 2) log 3 7 = (3 log 3 7) 2 = 7 2 = 49 (power of degree, basic logarithmic identity, definition of degree),
2) 7 2 log 7 3 = (7 log 7 3) 2 = 3 2 = 9 (…),
3) 10 3 log 10 5 = (10 log 10 5) 3 = 5 3 = 125 (…),
4) 0.1 2 log 0.1 10 = (0.1 log 0.1 10) 2 = 10 2 = 100 (…).
4.5 Basic properties of logarithms(slide 15)
You did a great job with the examples. Now calculate the following tasks written on the board:
a) log 15 3 + log 15 5 = ...,
b) log 15 45 – log 15 3 = …,
c) log 4 8 =…,
d) 7 = ... .
What do you think we need to know in order to perform operations with logarithms?
If students have difficulties, then ask the question: “In order to perform actions with degrees, what do you need to know?” (Answer: “Properties of degree”). Revisit the original question. (Properties of logarithms)
Here is a table with the properties of logarithms. It is necessary to give a name to each property and correctly formulate them.
slide 16
| № | The name of the property of logarithms | Properties of logarithms |
| 1. | unit logarithm. | log a 1 = 0, a > 0, a 1. |
| 2. | base logarithm. | log a a = 1, a > 0, a 1. |
| 3. | The logarithm of the product. | log a (xy) = log a x + log a y, a > 0, a 1, x > 0, y>0. |
| 4. | The logarithm of the quotient. | log a = log a x - log a y, a > 0, a1, x > 0, y > 0. |
| 5. | Degree logarithm. | log a x n = n log a x, x > 0, a > 0, a 1, nR. |
| 6. | Formula for moving to a new base | a > 0, a 1, b > 0, b 1, x > 0. |
5. Generalization and systematization of knowledge.
Slides 17-20
6. Homework.(slide 23)
7. Creative application of knowledge, skills and abilities.(slides 21 - 22)
Card work
8. Summing up.
Give answers to questions
- Formulate the definition of the logarithm and make the appropriate notation.
What types of logarithms exist? Record them.
– Write down the basic logarithmic identity.
- The origin of the word "logarithm". Who invented logarithms, in what year, brief information about them?
- Who introduced the logarithm with base e, which is called the natural logarithm?
What is the origin of the practice of using logarithms?
- Who and when invented the first slide rule, the first tables of logarithms?
