# How do you solve 2^(x) + 2^(2x) = 72?

Jun 22, 2016

$x = 3$

#### Explanation:

Taking $y = {2}^{x}$ we have

$y + {y}^{2} = 72$

Solving for $y$ we get

$\left\{y = - 9\right\} , \left\{y = 8\right\}$

but $y = {2}^{x}$ must be positive then we follow with

$y = {2}^{x} = 8 \to x = 3$