# How do you expand ln(x^2/y^2)?

Apr 30, 2016

$2 \ln x - 2 \ln y$

#### Explanation:

The first law of logs you will want to use is $\ln \left(\frac{a}{b}\right) = \ln a - \ln b$, so

$\ln \left({x}^{2} / {y}^{2}\right) = \ln {x}^{2} - \ln {y}^{2}$

Another law of logs is that an exponent inside the log is the same as a coefficient outside, or $\ln {c}^{2} = 2 \ln c$, so

$\ln {x}^{2} - \ln {y}^{2} = 2 \ln x - 2 \ln y$