Answer
$x=\frac{1}{3}$
Work Step by Step
We are asked to solve:
$\log_{8}{2}=x$
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=8, y=x, x=2$), we get:
$8^x=2$
Because we know that $2^3=8$ and $\sqrt[3]{8}=2$:
$x=\frac{1}{3}$
We confirm that the answer works:
$\log_{8}{2}=\frac{1}{3}$
$8^{\frac{1}{3}}=2$
$2=2$
