"Logarithms" Exponential function and logarithmic function PPT (Operations of logarithms in the second lesson)

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"Logarithms" Exponential function and logarithmic function PPT (Operations of logarithms in the second lesson)

Part One: Learning Objectives

Master the operational properties of logarithms and be able to use them to perform calculations related to logarithms

Understand the base-changing formula and be able to use the base-changing formula to convert general logarithms into natural logarithms or common logarithms

Be able to flexibly use the basic properties of logarithms, the operational properties of logarithms and the base-changing formula to solve logarithmic operations problems

Logarithmic PPT, part 2: independent learning

Problem guide

Preview textbooks P123-P126 and think about the following questions:

1. What are the three operational properties of logarithms?

2. How is the bottom changing formula expressed?

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).

■Instructions from famous teachers

For these three operational properties of logarithms, it should be noted that the equation is only true when all logarithms in the formula are meaningful. For example, log2[(-3)•(-5)]=log2(-3)+log2(-5) is wrong.

2. Bottom changing formula

logab＝__________ (a>0, and a≠1; c>0, and c≠1; b>0).

■Instructions from famous teachers

Remember the three common corollaries of the bottom-changing formula

(1) Corollary 1: logac·logca=1. This formula means that the real number and the base are interchanged, and the resulting logarithmic value and the original logarithmic value are reciprocals of each other.

(2) Corollary 2: logab·logbc·logca=1.

(3) Corollary 3: logambn=nmlogab. This formula means that the base becomes the original mth power, the real number becomes the original nth power, and the obtained logarithmic value is equal to nm times the original logarithmic value.

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1) The logarithms of products and quotients can be converted into the sum and difference of logarithms. ()

(2)loga(xy)＝logax·logay.()

(3)log2(-5)2＝2log2(-5). ()

It is known that a>0 and a≠1, then loga2+loga12=()

A． 0B.12

C. 1D． 2

Calculate log510-log52 equal to ()

A． log58 B． lg5

C. 1D． 2

Logarithmic PPT, the third part: lecture and practice interaction

Application of properties of logarithmic operations

Calculate the following equations:

(1)log5325;

(2)log2(32×42);

(3)log535-2log573+log57-log595;

(4)lg25＋23lg8＋lg5·lg20＋(lg2)2.

[Solution] (1) Original formula = 13log525 = 13log552 = 23.

(2) Original formula = log232 + log242 = 5 + 4 = 9.

(3) Original formula=log5(5×7)-2(log57-log53)+log57-log595=log55+log57-2log57+2log53+log57-2log53+log55=2log55=2.

(4) Original formula=2lg5+2lg2+(1-lg2)(1+lg2)+(lg2)2=2(lg5+lg2)+1-(lg2)2+(lg2)2=2+1=3.

regular method

Basic principles and methods of logarithmic simplification and evaluation

(1)Basic principles

Simplification and evaluation of logarithmic expressions generally use forward or inverse formulas to process real numbers. Which strategy to choose for simplification depends on the actual situation of the problem. It is generally carried out based on the principle of facilitating the simplification of real numbers.

(2) Two commonly used methods

① "Collect", convert 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 two logarithms with the same base.

Logarithmic PPT, Part 4: Feedback on Compliance

1. log242+log243+log244=()

A． 1B． 2

C. 24D.12

2. If a>0, a≠1, x>y>0, n∈N*, then the following formulas:

(1)(logax)n=nlogax;

(2)(logax)n=logaxn;

(3)logax=-loga1x;

(4)nlogax=1nlogax;

(5)logaxn=loganx.

Among them, the correct ones are ()

A． 2 B. 3

C. 4 D. 5

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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: 2024-11-09

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

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