# How do you solve the exponential equation 4^(2x)=4^(x+2)?

Feb 25, 2017

$x = 2.$

#### Explanation:

${4}^{2 x} = {4}^{x + 2} .$

$\Rightarrow {4}^{2 x} = {4}^{x} \cdot {4}^{2.}$

$\text{Dividing by } {4}^{x} \ne 0 , {4}^{2 x} / {4}^{x} = {4}^{2.}$

$\therefore {4}^{2 x - x} = {4}^{2.}$

$\therefore {4}^{x} = {4}^{2.}$

$\therefore x = 2.$

This soln. satisfy the given eqn.

The Soln. is $x = 2.$