# How do you solve the exponential equation 9^(2x+1)=3^(5x-1)?

##### 1 Answer
Mar 5, 2017

$x = 3$

#### Explanation:

Express the left side with a base of 3

$\Rightarrow {\left({3}^{2}\right)}^{2 x + 1} = {3}^{5 x - 1}$

$\Rightarrow {3}^{4 x + 2} = {3}^{5 x - 1}$

Since the bases are equal, we can equate the exponents.

$\Rightarrow 5 x - 1 = 4 x + 2$

$\Rightarrow x = 2 + 1 = 3$