# How do you solve log_2(x+5)-log_2(2x-1)=5?

Jul 13, 2016

I found: $x = \frac{37}{63}$

#### Explanation:

We can change the subtraction into a division of arguments and write:
${\log}_{2} \left(\frac{x + 5}{2 x - 1}\right) = 5$
then we use the definition of log to get rid of it and write:
$\frac{x + 5}{2 x - 1} = {2}^{5}$
$\frac{x + 5}{2 x - 1} = 32$
rearrange:
$x + 5 = 64 x - 32$
and:
$63 x = 37$
so:
$x = \frac{37}{63}$