# Logarithmic Equation: ( Log AX : Condition: 0  A  1 And X &gt; 0 ) Method 1: Same Base: Log AX  B  Log AYX = Y

Note: * Set tab x 0ab x 1

t

* There are 3 groups containing x => divided by the group with the largest or smallest base

4. Logarithmic function: y = log a x

+ TXD: x > 0

+ The function is uniform when a > 1

+ Inverse function when 0 < a < 1

5. PT Mǜ

Method 1: Same base: a x =b = a y <=> x = y

Method 2: Not with the same base: a x =b <=> x = log a b

Method 3: Set the secondary hidden: Aa 2x +ba x +C = 0

+ Set t a x ; t > 0

+ Solve for t => x

best

6. Logarithmic equation: ( log a x : Condition: 0 a 1 and x > 0 ) Method 1: Same base: log a x b log a y <=> x = y

Method 2: Not with the same base: log a x b <=> x = a b

Method 3: Set the secondary hidden: A. log 2 x B .log x C 0

a

a

+ Set t log a x ; there is no condition of t

+ Solve for t => x

7. Real pt mǜ and logarithm

Note: + Base a > 1: no direction change

+ Base 0< a < 1: change direction

8. Compound interest: A a (1 r ) n

3. Teach new lessons

Teacher's Activities

 Student Activities Content Activity 1. Investigate the properties of exponential functions, mǜ and mǜ functionslogarithmic function H1. Classify functions and state the conditions for their determination? D1.a) 3 x  3  0  D = R {1} b) x  1  0 2 x  3 D = (  ;1)   3 ;    2 c) x 2  x  12  0 D = (  ;  3)  (4;  )d) 25 x  5 x  0  D = [0; +∞) 1. Find the domain of the functiona) y  1 3 x  3 b) y  log x  1 2 x  3c) y  log x 2  x  12 d) y  25 x  5 x Activity 2. Consolidate logarithm calculations H1. What rules should be used? D1.a) log a x = 8b) log a x = 11 2. Givelog a b  3, log a c   2 . Calculate log a x with: a) x = a 3 b 2 cb) x = a 4 3 bc 3 Activity 3. Solve equations, mǜ inequalities, logarithms H1. If the solution? D1.a) Return to base 3 and 5. 3  x  5  3      x = –3 5   3  4. Solve the equations following submission: a) 3 x  4  3.5 x  3  5 x  4  3 x  3

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Teacher's Activities

 Student Activities Content  Note: x > 1 log 7 x  0 .H2. How to solve? b) Divide both sides by 16 x . 3  xLet t    , t > 0. 4  x = 1c) log 7 ( x  1)  0  x = 8d) log 3 x  3  x = 27D2.a) Return to the same base 2 .5 2  xLet t    , t > 0. 5 2 t 2  3 t  5  0  t  52 x < –1.b) Set t  log 0.2 x .t 2  5 t  6  0  2 < t < 3 0.008 < x < 0.04. b) 4.9 x  12 x  3.16 x  0 c)log 7 ( x  1) log 7 x  log 7 xd)log 3 x  log 3 x  log 1 x  6 35. Solve the following inequalities:a) (0, 4) x  (2.5) x  1  1.5 b)log 2 x  5log x   6 0.2 0.2 Activity 4. Consolidation

Emphasize:

- Calculate and change formulas

- How to solve equations, inequalities and logarithms.

- How to solve equations, inequalities and logarithms.

- Apply to general problems

IV. LEARN EXPERIENCE, SUPPLEMENT

+ Students take a long time to solve equations and often make mistakes

+ Students cannot solve the inequality.

APPENDIX 4

TEACHER: REVIEW CHAPTER II (EXPERIMENTAL CLASS)

I. OBJECTIVES

Knowledge

Exponential, mǜ and lgarithmic functions.

Rules for calculating factorials, mǜ and logarithms.

Solve equations, inequalities and logarithms

Skills

Investigate exponential functions, mǜ functions, and logarithmic functions.

Calculate expressions: Factor, mǜ, logarithm

Solve equations and inequalities.

Practice solving math problems using Casio FX 570 calculator

Attitude

Train carefulness, accuracy, quick reflexes, and quick prediction.

Think mathematical problems logically and systematically.

II. PREPARE

Teacher: Lesson plan. Exercise system.

Students: Textbooks, notebooks. Review all knowledge of chapter II

III. TEACHING ACTIVITIES

1. Stabilize the organization : Check class size.

2. Check the lesson:

1. Basic formulas

a n1

a n

a lo g a bb ;

log a

 

a

a . a a

log b log b

a

a

log a clog a blog a c

n

m a n a m

a

a

a

( ab ) a . b

log blog a b

a

first

log ( b . c ) log b log c

a

a

a

b

a

a

b

 

b

( a m ) n a m . n ( a n ) m

Change the base

log b

first

a

log a

b

log blog c b

a

log a

c

Derivative

( x n )' = nx n-1

( e x )' = e x

( a x )' = a x .lna

( u n )' = nu n-1 .u'

( e u )' = e u .u'

( a u )' = a u .lna.u'

( log x )' =

a

first

x .ln a

( log u )' =

a

1 . u '

u.ln a

2. Definite set of redundant functions: y = u

+ positive integer (Z + ) => u belongs to R

+ vowel or equal to 0 => u is different from 0

+ is not integer => u > 0

3. Function mǜ : y = a x

+ TXĐ: D = R

+ The function is uniform when a > 1

+ Inverse function when 0 < a < 1

; y = log a x

4. Logarithmic function: y = log a x

+ TXD: x > 0

+ The function is uniform when a > 1

+ Inverse function when 0 < a < 1

5. PT, BPT mǜ and logarithm

Method 1: Substitute the input with the CALC command

Method 2: Use the computer's search table with the command MODE 7 Note: + Base a > 1: does not change direction

+ Base 0< a < 1: change direction

6. Compound interest: A a (1 r ) n

3. Teach new lessons

Activities of teachers

 Student Activities Content Activity 1. Investigate the properties of exponential functions, mǜ and mǜ functionslogarithmic function Ask. Show how to choose the formula HD 1:Method 1: Students rememberMethod 2 : Calculator Choose x =2; m =3; n =4;y =5Pressing: 2 3 .2 4  2 3  4 will result in 0. So A is correct. Same for answers B and C HD 2 : Similar Select recipe1. Which of the following equations is incorrect?A. x m . x n  x m  nB.  x n  m  x n . mC.  xy  n  x n . y n D . x m . y n   xy  m  n . 2. Find the correct statement in the following statements: A. log a  x  y   log a x  log a y

Activities of teachers

 Student Activities Content HD 3 : according to the formulaHD 4 : How to find it?Students answer: x > 0HD 5:Method 1: Calculate Method 2: Calculator Choose x =2;a 2  x  a  2b  3 2 ; c  4 2Click on the expression to find answer DHD 6 : similar to HD 5 C. log 1  1a x log xa3. The function y  log x has a definite set3A. D  R B. D  R  0  C . D   0;   D. D    ;0 4. The function y  x  2 has a domain as:A. D    ;0  B. D  RC. D   0 ;   D . D  R  0  5. Given log a x  2, log b x  3, log c x  4 .Calculate the value of the expression: log x 5a 2 b cA. 12 B. 1 C. 6 D. 2413 9 13 76 .The value of the expressiona b  2  a b  1   a  3 b 3 2x  2 y  x  2 y  1  3To be:A. _ a 8 b 2 B . a 2 b 8 C . a 8 D . a 8 . b Activity 2. Train students to use computers