# How do you evaluate log_(1/15) (1/225)?

I found: ${\log}_{\frac{1}{15}} \left(\frac{1}{225}\right) = 2$
Here you need a number $x$ such that:
${\left(\frac{1}{15}\right)}^{x} = \frac{1}{225}$
You can find immediately that this number will be $x = 2$ in fact:
${\left(\frac{1}{15}\right)}^{2} = \frac{1}{225}$