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"Logarithmic Function" Exponential Function and Logarithmic Function PPT (Application of Logarithmic Function and Its Properties in Lesson 2)
Part One: Learning Objectives
Use the properties of logarithms and the monotonicity of logarithmic functions to compare sizes
Ability to solve inequalities using the monotonicity of logarithmic functions
Able to find the monotonicity of composite functions related to logarithmic functions
Can use the monotonicity of logarithmic functions and the substitution method to find
Solve range or minimum problems related to logarithmic functions
Logarithmic function PPT, part 2: interactive lecture and practice
Compare logarithmic values
Compare the two values in each of the following groups.
(1)ln0.3, ln2;
(2) loga3.1, loga5.2 (a>0, a≠1);
(3)log30.2, log40.2;
(4)log3π, logπ3.
[Solution] (1) Because the function y=lnx is an increasing function, and 0.3<2,
So ln0.3
(2) When a>1, the function y=logax is an increasing function on (0, +∞), and 3.1<5.2,
So loga3.1
When 0
So loga3.1>loga5.2.
regular method
Four methods commonly used when comparing logarithmic values
(1) Using the monotonicity of logarithmic functions with the same base.
(2) Use the graph of the logarithmic function or use the base-changing formula to convert the same real number.
(3) The base number and the real number are both different, so find the middle quantity.
(4) If the base is the same parameter, then the base will be classified and discussed based on its influence on the monotonicity of the logarithmic function.
Solving Logarithmic Inequalities
Solve the following inequalities:
(1)log17x>log17(4-x);
(2)logx12>1;
(3)loga(2x-5)>loga(x-1).
regular method
Solutions to two types of logarithmic inequalities
(1) An inequality of the form logaf(x)
①When 0g(x)>0;
②When a>1, it can be converted into 0
(2) An inequality of the form logaf(x)
①When 0ab;
②When a>1, it can be converted into 0
[Note] When solving problems related to logarithmic functions, the "domain first" principle must be followed.
Logarithmic function PPT, the third part: feedback on compliance with standards
1. The value range of the function y=2+log2x (x≥2) is ()
A． (3, +∞) B. (-∞,3)
C. [3, +∞) D. (-∞, 3]
2. The function y=lg|x| is ()
A． Even function, and monotonically increasing on the interval (-∞, 0)
B． Even function, and monotonically decreasing on the interval (-∞, 0)
C. Odd function, and monotonically increasing on the interval (0, +∞)
D. Odd function, and monotonically decreasing on the interval (0, +∞)
3. It is known that the maximum value of function f(x)=logax(0
A.14 B.22
C.24 D.12
4. The monotonic increasing interval of function f(x)=log5(2x+1) is ________.
5. It is known that the graph of the logarithmic function f(x) passes through the point (4, 2), try to solve the inequality f(2x-3)>f(x).
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