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Inverse, Exponential

and

Logarithmic Functions

Chapter 11

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11.5

Common and Natural Logarithms

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11.5 Common and Natural Logarithms

Objectives

1. Evaluate common logarithms using a calculator.

2. Use common logarithms in applications.

3. Evaluate natural logarithms using a calculator.

4. Use natural logarithms in applications.

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11.5 Common and Natural Logarithms

Common Logarithms

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11.5 Common and Natural Logarithms

Common Logarithms

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11.5 Common and Natural Logarithms

Evaluating Common Logarithms

The loudness of sound in decibels is given by the formula

Where I0 is the weakest sound detected by the observer and I is the intensity of the given sound.

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11.5 Common and Natural Logarithms

Common Logarithms in Applications

0

10logI

yI

That is, find the value of I0 is 51,000 times I.

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11.5 Common and Natural Logarithms

Common Logarithms in Applications

0

10logI

yI

0

51,00010logy

I

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11.5 Common and Natural Logarithms

Natural Logarithms and Evaluation

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11.5 Common and Natural Logarithms

Natural Logarithms and Evaluation

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11.5 Common and Natural Logarithms

Applications of Natural Logarithms