Answer
$ x\approx 4.52$
Work Step by Step
$8^{x}=12,143$
We can't show the RHS as a power of 8, so we apply $\log_{8}($...$)$ to both sides
$\log_{8}8^{x}=\log_{8}12,143\qquad $ ... apply basic property, $\log_{b}b^{x}=x $
$ x=\log_{8}12,143$
if your calculator has only $\ln $ and $\log $, apply the change of base property, $\displaystyle \log_{b}M=\frac{\log_{a}M}{\log_{a}b}$
and round to two decimal places:
$ x=\displaystyle \frac{\log 12,143}{\log 8}\approx 4.52$
