# How do you write 5^-3 = 1/125 in log form?

$\log {10}^{{5}^{- 3}} = \ln {e}^{{5}^{- 3}} = {\log}_{b} {b}^{{5}^{- 3}}$
Use ${\log}_{b} {b}^{n} = n {\log}_{b} b = n \left(1\right) = n$
Here, $n = {5}^{- 3}$ and b is at your choice...