# How do you solve 9^(x-1)=3^x?

Apr 29, 2015

$x = 2$

Solution

${9}^{x - 1} = {3}^{x}$

Making bases of both sides equal

As 9 can be written as $9 = {3}^{2}$

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

It must be equal to

$2 \left(x - 1\right) = x$

$2 x - 2 = x$

$2 x - x = 2$

$x = 2$