 Section 3.2 Logarithmic Functions. The Logarithmic Function.

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Section 3.2 Logarithmic Functions

The Logarithmic Function

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

Important Equivalency Is equivalent to

Convert From Logarithmic to Exponential

Convert from Exponential to Logarithmic

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.

Evaluate the Following Log Expressions

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

Evaluate the Following Log Expressions

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.

Find the domain of each logarithmic function

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)

Evaluate the Following Log Expressions

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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