dang logs!
You only have to change $\displaystyle \sqrt[9]{27}$ into an expression with the base 3. The exponent of this expression is the logarithm you are looking for:
$\displaystyle \sqrt[9]{27} = \left(3^{3}\right)^{\frac19}$
I'm a bit curious: I know decimal logarithms and natural logarithms but I have never heard about dang logarithms