What is the next step in solving this (using this method)? But there is another way which involves using the log laws (which I know how to do).

$\displaystyle \log x - \dfrac{1}{3}\log8 = \log7$

$\displaystyle 10^{\log(x)- \frac{1}{3}\log8} = 10^{\log7}$

I believe the next step involves dividing the bases of the exponents, since the exponents are subtracted.