# How do you write 3lna - 6lnb as a single logarithm?

Sep 1, 2015

$3 \ln \left(a\right) - 6 \ln \left(b\right) = \ln \left[\frac{{a}^{3}}{{b}^{6}}\right]$
$3 \ln \left(a\right) - 6 \ln \left(b\right) \implies$ use law of logs : $\log \left({m}^{n}\right) = n \log \left(m\right) :$
$= \ln \left({a}^{3}\right) - \ln \left({b}^{6}\right) \implies$ use: $\log \left(m\right) - \log \left(n\right) = \log \left(\frac{m}{n}\right) :$
$= \ln \left[\frac{{a}^{3}}{{b}^{6}}\right]$