# How do you condense 3 ln 3 + ln 9?

Apr 6, 2016

$\ln 243$

#### Explanation:

$1$. Start by using the natural logarithmic property, ${\ln}_{\textcolor{p u r p \le}{b}} \left({\textcolor{red}{m}}^{\textcolor{b l u e}{n}}\right) = \textcolor{b l u e}{n} \cdot {\ln}_{\textcolor{p u r p \le}{b}} \left(\textcolor{red}{m}\right)$, to simplify $3 \ln 3$.

$3 \ln 3 + \ln 9$

$= \ln \left({3}^{3}\right) + \ln \left(9\right)$

$2$. Use the natural logarithmic property, ${\ln}_{\textcolor{p u r p \le}{b}} \left(\textcolor{red}{m} \cdot \textcolor{b l u e}{n}\right) = {\ln}_{\textcolor{p u r p \le}{b}} \left(\textcolor{red}{m}\right) + {\ln}_{\textcolor{p u r p \le}{b}} \left(\textcolor{b l u e}{n}\right)$, to simplify the expression.

$= \ln \left({3}^{3} \cdot 9\right)$

$3$. Simplify.

$= \ln \left(27 \cdot 9\right)$

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \ln 243 \textcolor{w h i t e}{\frac{a}{a}} |}}}$