# Simplyfy ln(1/90) in terms of ln?

Mar 25, 2017

$- \left[\textcolor{w h i t e}{.} 2 \ln \left(3\right) + \ln \left(2\right) + \ln \left(5\right) \textcolor{w h i t e}{.}\right]$

#### Explanation:

This is the same as $\ln \left(1\right) - \ln \left(90\right)$

but $\ln \left(1\right) = 0$ so we only need to consider $- \ln \left(90\right)$

Lets consider $90 \to 3 \times 30 = 3 \times 3 \times 10 = 3 \times 3 \times 2 \times 5$

So we have:

$- \left[\textcolor{w h i t e}{.} 2 \ln \left(3\right) + \ln \left(2\right) + \ln \left(5\right) \textcolor{w h i t e}{.}\right]$