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Convert between Exponential and Logarithmic Equations Solutions

• Exponential equations and logarithmic equations are    inverses    of one another.
• To define exponential and logarithmic equations:
  $\begin{array}{cccc}{\log }_b y=x& & & b^x=y\end{array}$
  • b is called the    base    and $b>0, b\ne 1$.
  • x is called the    power    or exponent. 
  • y is called the    argument    or the answer and $y>0$.

Note

Note: When working with logarithms, y will be referred to as the argument, so it is not confused with a solved value(s).

•    Converting    an exponential equation to a logarithmic equation, and vice versa, allows you to work with both exponential and logarithmic equations.

• When working with logs, think:    b    multiplied by itself    x    times results in    y   .
• In words, “base b raised to the x power    equals    y” and “log base b of y    equals    x”

Convert equation from exponential to logarithmic	Convert equation from logarithmic to exponential
$b^x=y\begin{array}{cc}& \end{array}{\log }_b y=x$	$\begin{array}{cccc}{\log }_b y=x& & & b^x=y\end{array}$

Example 1

Convert each equation to the equivalent logarithmic form.


Example 2

Convert each equation to the equivalent exponential form.