# 13.2 Logarithmic Functions

**Exponential Form • Logarithmic Form • Logarithmic Function • Graphing Logarithmic Functions • Features of Logarithmic Functions • Inverse Functions**

For many uses in mathematics and for many applications, it is necessary to express the exponent `x` in the exponential function $y\hspace{0.17em}=\hspace{0.17em}{b}^{x}$ in terms of `y` and the base `b`. This is done by defining a *logarithm.* Therefore, *if* $y\hspace{0.17em}=\hspace{0.17em}{b}^{x}\hspace{0.17em},\hspace{0.17em}$ *the exponent x is the* **logarithm** *of the number y to the base b.* We write this as

**(13.2)**

This means that `x` is the power to which the base `b` must be raised in order to equal the number `y`. That is, `x` is a logarithm, and ** a logarithm is an exponent.** As with the exponential function, for the equation $x\hspace{0.17em}=\hspace{0.17em}{\text{log}}_{b}y\hspace{0.17em},\hspace{0.17em}\text{}x$ may be ...

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