# What is x if log_2(x)+Log_2(x-7)=3?

Nov 7, 2015

I found $x = 8$

#### Explanation:

We can use a property of logs to write it as:
${\log}_{2} \left(x \left(x - 7\right)\right) = 3$
we then use the definition of log to get:
$x \left(x - 7\right) = {2}^{3}$
${x}^{2} - 7 x = 8$
${x}^{2} - 7 x - 8 = 0$
Two solutons (using the Quadratic Formula):
${x}_{1} = 8$
${x}_{2} = - 1$ this will give a negative argument in the log.