# How do you solve 12^(y-2) =20?

Aug 23, 2016

$y = \ln \frac{2880}{\ln} 12$

#### Explanation:

Take the natural logarithm of both sides.

$\ln \left({12}^{y - 2}\right) = \ln 20$

$\left(y - 2\right) \ln 12 = \ln 20$

$y \ln 12 - 2 \ln 12 = \ln 20$

$y \ln 12 = \ln 20 + \ln 144$

$y = \ln \frac{2880}{\ln} 12$

Hopefully this helps!