"Logarithms" Exponential function and logarithmic function PPT courseware (the concept of logarithms in the first lesson)

Description

"Logarithms" Exponential function and logarithmic function PPT courseware (the concept of logarithms in the first lesson)

Part One: Learning Objectives

1. Understand the concept of logarithms, master the properties of logarithms, and be able to perform simple logarithmic calculations. (main difficulty)

2. Understand the equivalence relationship between exponential and logarithmic expressions, and be able to convert logarithmic and exponential expressions into each other. (emphasis)

3. Understand the concepts and notation of common logarithms and natural logarithms.

core competencies

Cultivate mathematical operation literacy by using the mutual conversion of exponential and logarithmic expressions and applying the properties of logarithms to solve problems.

Logarithmic PPT, part 2: independent preview to explore new knowledge

A preliminary exploration of new knowledge

1. logarithm

(1) Interconversion of exponential and logarithmic expressions and related concepts:

(2)The range of base a is___________.

2. Common logarithms and natural logarithms

3. Basic properties of logarithms

(1) Negative numbers and zero ____ logarithms.

(2)loga 1=____(a>0, and a≠1).

(3)logaa=____(a>0, and a≠1).

Think: Why do zero and negative numbers not have logarithms?

Tip: According to the definition of logarithm: ax=N (a>0 and a≠1), there is always N>0, so when converted into logarithm x=logaN, there is no case of N≤0.

First try

1. If a2=M (a>0 and a≠1), then there is ()

A． log2M＝a

B． logaM＝2

C. log22＝M

D. log2a＝M

2. If log3x=3, then x=()

A． 1

B． 3

C. 9

D. 27

3. In b=loga(5-a), the value range of real number a is ()

A． a>5 or a<0

B． 0

C. 0

D. 1

Logarithmic PPT, the third part: cooperative exploration to improve literacy

Interconversion of exponential and logarithmic forms

[Example 1] Format the following logarithms into exponential form or exponential into logarithmic form:

(1)2-7=1128; (2)log1232=-5;

(3) lg 1 000 = 3; (4) ln x = 2.

regular method

Methods of converting exponential and logarithmic forms into each other

1To convert the exponential expression into a logarithmic expression, you only need to treat the power as a real number, the exponent as a logarithmic value, the base remains unchanged, and write the logarithmic expression;

2To convert the logarithm into an exponential form, just use the real number as the power, the logarithm as the exponent, keep the base unchanged, and write the exponential form.

Use the relationship between exponential and logarithmic expressions to evaluate

[Example 2] Find the value of x in the following formulas:

(1)log64x＝-23; (2)logx 8＝6;

(3)lg 100＝x; (4)-ln e2＝x.

regular method

Steps to find the value of logarithmic expression logaNa>0, and a≠1, N>0

1Suppose logaN=m;

2Write logaN=m as exponential form am=N;

3Write N as an exponential power with a as the base N=ab, then m=b, that is, logaN=b.

Class summary

1. The concept of logarithms: ab=N⇔b=logaN (a>0 and a≠1) is a useful tool for solving exponential and logarithmic problems.

2. The mutual conversion of exponential and logarithmic expressions reflects the idea of ​​equivalent transformation in mathematics. When it comes to the evaluation of logarithmic expressions, it is often transformed into an arithmetic problem of exponential power.

3. The logarithmic identity alogaN=N, the conditions for its establishment are a>0, a≠1, N>0.

Logarithmic PPT, the fourth part: reaching the standard in class and solidifying the double base

1. Thinking and analysis

(1) logaN is the product of loga and N. ()

(2)(-2)3＝-8 can be converted into log(-2)(-8)＝3.()

(3) The essence of logarithmic operation is to find the exponent. ()

(4) In b=log3(m-1), the value range of real number m is (1, +∞). ()

2. The following incorrect conversion of exponential and logarithmic expressions is ()

A． 100＝1 and lg 1＝0

B． 27-13=13 and log2713=-13

C. log39=2 and 912=3

D. log55=1 and 51=5

3. If log2(logx9)=1, then x=________.

4. Find the value of x in each of the following equations:

(1)logx27=32; (2)log2 x=-23;

(3)x=log2719; (4)x=log1216.

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For more information about the PPT courseware "Concepts of Logarithms and Logarithms of Exponential Functions and Logarithmic Functions", please click on the ppt tag of Exponential Functions and Logarithmic Functions ppt Logarithms ppt Concepts of Logarithms.

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Update Time: 2024-06-30

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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