What is a Logarithm?

C. Hunter

Principles of Math 12

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2log 8 33log 81 4

5log 125 3 6log 36 2

2log 32 5 10log 100 2

What is the relationship between the three numbers?

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logaccb ba

If logab = c, then what is the relationship between the variables?

base exponent

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logbaseanswer = exponent

logbaconand = eggs

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Evaluate and explain.

1. 2.

3. 4.

5. 6.

7.

7log 49 4log 64

2

1log

8

1log10000

3log 1 125log 5

76log 6

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Solve.

1. 2log 6x 62 x Exponential form

64 x

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2. 5

1log

625x

15

625x Exponential form

4x

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3. log 343 3x

3 343x Bacon and Eggs

3 343x

7x

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Exponential & Logarithmic Functions

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The Richter Scale is a base 10 logarithmic scale.

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An earthquake in Seattle measured 5.4. An earthquake in Vancouver measured 3.2. How many times as intense was the earthquake in Seattle as the one in Vancouver?

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5.4

3.2

10

10S

V

I

I

5.4 3.210

2.210

158