Writing Equivalent Logarithmic and Exponential Equations

Here is a table of several pairs of equivalent statements, written in both logarithmic and exponential forms:

Logarithmic Form	Exponential Form
$\log_28=3$	$2^3=8$
$\log_{\frac{1}{2}}16=-4$	$\left(\frac{1}{2}\right)^{-4}=16$
$\log_{10}100,000=5$	$10^5=100,000$
$\log_3\frac{1}{81}=-4$	$3^{-4}=\frac{1}{81}$
$\log_55=1$	$5^1=5$
$\log_{\frac{3}{4}}2=0$	$\left(\frac{3}{4}\right)^0=1$

To remember the relationships among $a,\:x,\:$and $y$ in the two equivalent forms $y=\log_ax\:$and $x=a^y,\:$refer to these two diagrams below: