If the equation written like this
[tex]log x^{ \frac{1}{8} } = - \frac{3}{2}
then
10^{- \frac{3}{2} } = x^{ \frac{1}{8} }
(10^{- \frac{3}{2} })^{8} = ( x^{ \frac{1}{8} } )^{8}
x= 10^{-3*4} = 10^{-12}
x=10^{-12}
If the equation looks like this , then it has the solution
x=10^{-12}[/tex]