# How do you solve Log_2 x^7=21?

May 28, 2016

$x = 8$

#### Explanation:

Using basic properties of logs we find:

$21 = {\log}_{2} {x}^{7} = 7 {\log}_{2} x$

Dividing both ends by $7$ we have:

$3 = {\log}_{2} x$

So:

${2}^{3} = {2}^{{\log}_{2} x} = x$

That is:

$x = {2}^{3} = 8$