Logarithms

Logarithms

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Learning without value, how useful it is, seems to be just going to create a smarter demon.(C.S. Lewis)

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Outline

Define of Logarithms

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Wrong answer

Definition of Logarithms

Law of Logarithms

Evaluation

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Law of Logarithms

Think??

the inverse of exponential function

Definiton of logarithm

Exponent

y = ax

Base

Argument

alog y = x

Example

Rewrite using a logarithms a. 44=256 b. 111 = 11

Example

Rewrite using a power 2log⁡ 16 =4 5log ⁡25 =2

Example

Without using a calculator, find the value of a) 2log ⁡8 b) 3log⁡ 81

Law of Logarithms

Law 1

𝑎log ⁡𝑥 + alog⁡ 𝑦= 𝑎log⁡(𝑥.𝑦) 𝑎log ⁡𝑥 − 𝑎log⁡ 𝑦= 𝑎log⁡( 𝑥/𝑦)

Example

Finding the value of a) 2log⁡ 8 + 2log⁡ 4= b) 2log ⁡8 − 2log 4= c) 3log⁡ 3 + 3log⁡ 9= d) 4log⁡ 5 + 6log⁡ 5 =

Law 2

𝑎 log⁡𝑏 = 𝑦/𝑥 𝑎log⁡𝑏

example

4 log⁡ 81

2 5log⁡ 3 + 3 5log ⁡2

evaluation Let's Play Game!

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02

ammunition or bullets can be obtained if they run out if they succeed in answering the questions given.

03

Conclusion

1) The rule of logarithms is within the rule of God2) Logarithms reflect the regularity of God in the universe

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