"Logarithms" Exponential function and logarithmic function PPT courseware (Operations of logarithms in lesson 2)

Description

"Logarithms" Exponential function and logarithmic function PPT courseware (Operations of logarithms in lesson 2)

Part One: Learning Objectives

1. Understand the operational properties of logarithms. (emphasis)

2. You can use the base-changing formula to convert general logarithms into natural logarithms or common logarithms. (difficulty)

3. Will use the properties of operations to perform some simple simplifications and proofs. (easy to mix)

core competencies

1. Use the operational properties of logarithms to simplify and evaluate, and cultivate mathematical operation literacy.

2. Cultivate logical reasoning skills by learning the bottom-changing formula.

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

A preliminary exploration of new knowledge

1. Operational properties of logarithms

If a>0, and a≠1, M>0, N>0, then:

(1)loga(MN)=______________;

(2)logaMN=______________;

(3)logaMn=__________(n∈R)．

Thinking: When M>0, N>0, loga(M+N)=logaM+logaN, loga(MN)=logaM·logaN, are they true?

2. Logarithmic base conversion formula

If a>0 and a≠1; c>0 and c≠1; b>0,

Then there is logab=______.

First try

1. Calculate log84+log82 equals ()

A． log86　B． 8

C. 6D. 1

2. Calculate log510-log52 equal to ()

A． log58 B. lg 5

C. 1 D． 2

3. log23•log32=________.

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

Application of properties of logarithmic operations

[Example 1] Calculate the values ​​of the following formulas:

(1)12lg 3249-43lg 8+lg 245;

(2)lg 52＋23lg 8＋lg 5•lg 20＋(lg 2)2;

(3)lg 2＋lg 3－lg 10lg 1.8.

regular method

1. The key to solving problems using the properties of logarithms is to turn differences into similarities. First, make the bases of each item the same, and then find the connection between the real numbers.

2. For complex calculation formulas, you can simplify them first and then calculate them. Common methods for simplifying problems:

(1) "Split": Split the logarithm of the product (quotient) into the sum (difference) of two logarithms;

(2) "Collect": convert the sum (difference) of logarithms with the same base into the logarithm of the product (quotient).

Logarithmic base conversion formula

[Example 2] (1) Calculation:

(log2125+log425+log85)•(log1258+log254+log52).

(2) It is known that log189=a,18b=5, find log3645 (expressed by a, b).

[ Solution +1)log52＝133·3＝13.

Class summary

1. By applying the arithmetic rules of logarithms, higher-level operations (multiplication, division, exponentiation) can be transformed into lower-level operations (addition, subtraction, multiplication).

2. The base-changing formula reflects the idea of ​​reduction in mathematics, and its essence is to transform logarithmic operations with different bases into logarithmic operations with the same base.

3. Be proficient in the operation rules of logarithms, and pay attention to the difference in memory of the same exponential operation rules.

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

1. Thinking and analysis

(1)log2x2＝2log2x.()

(2)loga[(-2)×(-3)]＝loga(-2)+loga(-3)． ()

(3)logaM•logaN=loga(M+N). ()

(4)logx2＝1log2x.()

2. Calculate log92·log43=()

A． 4B． 2

C.12 D.14

3. Assume 10a=2, lg 3=b, then log26=()

A.ba B.a＋ba

C. abD． a+b

4. Calculation: (1)log535-2log573+log57-log51.8;

(2)log2748+log212-12log242-1.

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

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Update Time: 2024-07-09

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

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