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Section 3.2 Logarithmic Functions

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The Logarithmic Function

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The Big Idea The logarithmic function is the inverse of the exponential function.

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Important Equivalency Is equivalent to

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Convert From Logarithmic to Exponential

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Convert from Exponential to Logarithmic

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How to Find Logs 1.Use what you know. If you know that 2 to the 3 rd power is 8, then you also know that the log, base 2, of 8 is 3. 2.Use properties of exponents and radicals. Taking the square root of something is the same as raising that same thing to the ½ power. And fractions can often be re-written using negative exponents.

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Evaluate the Following Log Expressions

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How to Find Logs, continued 3.Use these helpful log properties:

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Evaluate the Following Log Expressions

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The domain of a logarithmic function It is not possible to take the log of a negative number. To find the domain of a logarithmic function, set the “argument” > 0.

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Find the domain of each logarithmic function

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Natural and Common Logs Logs to the base of 10 are called common logs (log on your calculator) Logs to the base of e are called natural logs (ln on your calculator)

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Evaluate the Following Log Expressions

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Graphs of Logarithmic Functions You may omit questions dealing with graphs on both the homework (15 – 18) and the quiz (6 and 7). I will give you credit for those questions.

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