# How do you solve 4-4 + log _ 9 (3x - 7) = 6?

Dec 29, 2015

$x = \frac{{9}^{6} + 7}{3}$

#### Explanation:

$\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} + {\log}_{9} \left(3 x - 7\right) = 6$

$\implies {\log}_{9} \left(3 x - 7\right) = 6$

To undo the logarithm with base $9$, exponentiate each side.

$\implies {9}^{{\log}_{9} \left(3 x - 7\right)} = {9}^{6}$

$\implies 3 x - 7 = {9}^{6} = 531441$

$\implies 3 x = 531448$

$\implies x = \frac{531448}{3} = 177149 \frac{1}{3}$

This can also be written as $x = \frac{{9}^{6} + 7}{3}$.