# How do you solve log x^3 + log 8 =3?

Aug 4, 2015

I found: $x = 5$

#### Explanation:

Supposing your logs with base $10$ and considering the property of the sum of logs you can write:
${\log}_{10} \left({x}^{3} \cdot 8\right) = 3$
$8 {x}^{3} = {10}^{3}$
${x}^{3} = {10}^{3} / 8$ taking the cube root on both sides you get:
$\sqrt[3]{{x}^{3}} = \sqrt[3]{{10}^{3} / 8}$
So:
$x = \frac{10}{2} = 5$