# How do you solve 2^x= 4^(x+1)?

Sep 9, 2015

color(blue)(x = -2

#### Explanation:

${2}^{x} = {4}^{x + 1}$

We know that $4 = {2}^{2}$

So,
${2}^{x} = {2}^{2 \left(x + 1\right)}$

2^color(blue)(x) = 2^color(blue)((2x +2 )

At this stage as the bases are equal we equate the exponents to find $x$

$x = 2 x + 2$
$- 2 = 2 x - x$
color(blue)(x = -2