# 5.3 Logarithmic Functions and Graphs

Find common logarithms and natural logarithms with and without a calculator.

Convert between exponential equations and logarithmic equations.

Change logarithmic bases.

Graph logarithmic functions.

Solve applied problems involving logarithmic functions.

We now consider *logarithmic*, or *logarithm, functions*. These functions are inverses of exponential functions and have many applications.

# Logarithmic Functions

We have noted that every exponential function (with $a>0$ and $a\ne 1$) is one-to-one. Thus such a function has an inverse that is a function. In this section, we will name these inverse functions logarithmic functions and use them in applications. We can draw the graph of the inverse of an exponential function ...

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