Question 674118
Notice log(a^b) = b*log(a) by our power property of logarithms.

We have {{{(1/3)log(x+2)}}} but that is {{{log(((x+2)^(1/3)))}}}

So,  {{{log(((x+2)^(1/3))) = log(8)}}}

Log is usually noted as base 10, so exponentiate both sides by 10.

10^log((x+2)^(1/3)) = {{{10^(log(8))}}} 

{{{(x+2)^(1/3) = 8}}}

Cube both sides.

{{{x+2 = 8^3}}}

{{{x+2 = 512}}}

{{{x = 510}}}

Check:

(1/3) * log(510+2) = (1/3) log(512) = .9031

log(8) = .9031