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 = bx in terms of y and the base b. This is done by defining a logarithm. Therefore, if y = bx ,  the exponent x is the logarithm of the number y to the base b. We write this as

If y = bx ,  then x = logby .  (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 = logby ,  x may be ...

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