# How do you write 9^(3/2) = 27 in log form?

${\log}_{9} \left(27\right) = \frac{3}{2}$
For $b > 0$, $b \ne 1$ and $y > 0$, the symbol $x = {\log}_{b} \left(y\right)$ represents the unique real number such that ${b}^{x} = y$ (it's the unique solution of that equation).
Since $x = \frac{3}{2}$ is the unique solution of the equation ${9}^{x} = 27$, it follows that ${\log}_{9} \left(27\right) = \frac{3}{2}$.