# How do you solve log_2( 2x) + log _ 2 x = 5?

Nov 27, 2015

I found $x = 4$

#### Explanation:

We can use the property of logs relating the sum with the product of the arguments and write:
${\log}_{2} \left(2 x \cdot x\right) = 5$
use the definition of log:
$2 {x}^{2} = {2}^{5}$
${x}^{2} = \frac{32}{2}$
$x = \pm \sqrt{16} = \pm 4$
only the positive one is acceptable.