"End of Chapter Review Improvement Course" Exponential Function and Logarithmic Function PPT

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"End of Chapter Review Improvement Course" Exponential Function and Logarithmic Function PPT

Comprehensive improvement

Exponential and logarithmic operations

Find the values ​​of the following expressions:

(1)827-23-3e•e23+(2-e)2+10lg 2;

(2)lg25＋lg 2×lg 500－12lg125－log29×log32.

[Solution] (1)827-23-3e•e23+(2-e)2+10lg 2

=233-23-e13•e23+(e-2)+2

=23-2-e+e-2+2=322=94.

(2)lg25＋lg 2×lg 500－12lg125－log29×log32

＝lg25＋lg 2×lg 5＋2lg 2－lg15－log39

=lg 5(lg 5+lg 2)+2lg 2-lg 2+1-2

＝lg 5＋lg 2-1＝1-1＝0.

regular method

(1) Principles to be followed in the operations of exponents and logarithms

①Exponent operation: Pay attention to the order of simplification. Generally, negative exponents are converted into positive exponents first, and the radical expression is converted into a fractional exponent power operation. In addition, if a fraction appears, attention should be paid to factoring the numerator and denominator to achieve the purpose of reduction;

②Operation of logarithms: Pay attention to the changes in the range during the application of the formula. The front and back must be equivalent. Generally, it is carried out based on the principle of simplification of real numbers.

(2) Two basic methods to simplify logarithms with the same base

① "Collect": Take the sum (difference) of two pairs of numbers with the same base into the logarithm of the product (quotient);

② "Split": Split the logarithm of the product (quotient) into the sum (difference) of the logarithms.

Graph problems of exponential functions and logarithmic functions

If the graph of function y=logax(a>0, and a≠1) is as shown in the figure, then the correct graph of the following function is ()

[Analysis] According to the meaning of the question, the image of y=logax (a>0, and a≠1) passes through the point (3, 1), and it can be solved that a=3. In option A, y=3-x=13x, obviously The image is wrong; in option B, y=x3, which can be seen from the power function image is correct; in option C, y=(-x)3=-x3, which is obviously inconsistent with the drawn image; in option D, y=log3 The image of (-x) is symmetrical about the y-axis and the image of y=log3x, which is obviously inconsistent. Therefore choose B.

regular method

(1) The image of the identification function starts from the following aspects:

① Monotonicity: the changing trend of the function image;

②Parity: the symmetry of the function graph;

③The function value corresponding to the special point.

(2) To find the range of parameters for equations or inequalities that are known to be unsolvable, the idea of ​​combining numbers and shapes is often used to solve the problem.

Track training

1. It is known that a>1, b<-1, then the image of function y=loga(x-b) does not go through ()

A． First QuadrantB. second quadrant

C. The third quadrant D. Quadrant 4

2. For all positive real numbers a>0 and a≠1, the graph of the function y=ax+1-2 must pass through a certain point, then the coordinates of the fixed point are ________.

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Update Time: 2024-10-19

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