# Question #c83cc

Apr 11, 2017

$\textcolor{b l u e}{x = 84}$

#### Explanation:

I'm assuming you mean $- 6 {\log}_{3} \left(x - 3\right) = - 24$

Divide both sides by $- 6$.

$\left[1\right] \text{ } - 6 {\log}_{3} \left(x - 3\right) = - 24$

$\left[2\right] \text{ } \frac{\textcolor{red}{\cancel{- 6}} {\log}_{3} \left(x - 3\right)}{\textcolor{red}{\cancel{- 6}}} = \frac{\textcolor{red}{\cancel{- 24}} 4}{\textcolor{red}{\cancel{- 6}}}$

$\left[3\right] \text{ } {\log}_{3} \left(x - 3\right) = 4$

We will now change this to its equivalent exponential form. Take note that $y = {b}^{x} \iff {\log}_{b} y = x$

$\left[4\right] \text{ } \iff {3}^{4} = x - 3$

$\left[5\right] \text{ } 81 = x - 3$

$\left[6\right] \text{ } 81 + 3 = x$

$\left[7\right] \text{ } \textcolor{b l u e}{x = 84}$