# How do you solve the exponential equation 9^(2x)=27^(x-1)?

Mar 3, 2017

$x = - 3$

#### Explanation:

Express the equation in $\textcolor{b l u e}{\text{bases of 3}}$

$\Rightarrow {\textcolor{b l u e}{\left({3}^{2}\right)}}^{2 x} = {\textcolor{b l u e}{\left({3}^{3}\right)}}^{x - 1}$

$\Rightarrow {3}^{4 x} = {3}^{3 x - 3}$

We can now equate the exponents.

$\Rightarrow 4 x = 3 x - 3$

$\Rightarrow x = - 3$