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

Jul 8, 2015

color(blue)(x=2

#### Explanation:

${9}^{2 x - 1} = {3}^{2. \left(2 x - 1\right)} = {3}^{4 x - 2}$

${27}^{x} = {3}^{3 x}$

Upon equating:

${3}^{4 x - 2} = {3}^{3 x}$
Since the base is equal , we can equate the powers:

$4 x - 2 = 3 x$
color(blue)(x=2