Note: * Set t a b x 0 a b 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 functions logarithmic 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 function a) y 1 3 x 3 b) y log x 1 2 x 3 c) 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 = 8 b) log a x = 11 
2. Give log a b 3, log a c 2 . Calculate log a x with: a) x = a 3 b 2 c b) x = a 4 3 b c 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 x Let t , t > 0. 4 x = 1 c) log 7 ( x 1) 0 x = 8 d) log 3 x 3 x = 27 D2. a) Return to the same base 2 . 5 2 x Let t , t > 0. 5 2 t 2 3 t 5 0 t 5 2 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 x d) log 3 x log 3 x log 1 x 6 3 5. 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 n 1
a n
a lo g a b b ;
log a
a
a . a a
log b log b
a
a
log a c log a b log a c
n
m a n a m
a
a
a
( ab ) a . b
log b log 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 b log c b
a
log a
c
Derivative
( x n )' = nx n1
( e x )' = e x
( a x )' = a x .lna
( u n )' = nu n1 .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 functions logarithmic function 

Ask. Show how to choose the formula 
HD 1: Method 1: Students remember Method 2 : Calculator Choose x =2; m =3; n =4; y =5 Pressing: 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 recipe 1. Which of the following equations is incorrect? A. x m . x n x m n B. x n m x n . m C. 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 formula HD 4 : How to find it? Students answer: x > 0 HD 5: Method 1: Calculate Method 2: Calculator Choose x =2; a 2 x a 2 b 3 2 ; c 4 2 Click on the expression to find answer D HD 6 : similar to HD 5 
C. log 1 1 a x log x a 3. The function y log x has a definite set 3 A. 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 R C. 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 5 a 2 b c A. 12 B. 1 C. 6 D. 24 13 9 13 7 6 .The value of the expression a b 2 a b 1 a 3 b 3 2 x 2 y x 2 y 1 3 To 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 