Section 5.2 Logarithmic Functions

Section Objectives

  1. Evaluate logarithmic functions.
  2. Graph logarithmic functions.
  3. Use properties of logarithms to simplify expressions.



Logarithmic Functions

The logarithmic functions are the inverses of the exponential functions.


To more specific...

Let be a fixed positive real number not equal to 1. The logarithmic function with base-, denoted , is the inverse of the base- exponential function. That is,



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Properties of the Logarithmic Functions

Because the logs and exponentials are inverses, we must have:



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In general, the logarithmic functions have the following properties.






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The Natural Logarithm

The base- logarithm is called the natural logarithm:


Your scientific calculator has built-in functions to compute base-10 and base- exponentials and logarithms.



Using the Properties of Logs

The properties of logarithms can be very useful when evaluating expressions and solving equations.


Examples