# How do I solve this? Thank you!

Nov 8, 2016

$x = {2}^{13} = 8 , 192$

#### Explanation:

The logs are all to the same base.

$\textcolor{b l u e}{5} {\log}_{2} 4 + {\log}_{2} 8 = {\log}_{2} x \text{ } \leftarrow$ use the power law

${\log}_{2} {4}^{\textcolor{b l u e}{5}} + {\log}_{2} 8 = {\log}_{2} x$

If logs are being added, numbers are multiplied...

${\log}_{2} \left({4}^{5} \times 8\right) = {\log}_{2} x \text{ } \leftarrow$ change to powers of 2

${\log}_{2} \left({\left({2}^{2}\right)}^{5} \times {2}^{3}\right) = {\log}_{2} x$

${\log}_{2} \left({2}^{10} \times {2}^{3}\right) = {\log}_{2} x$

${\log}_{a} B = {\log}_{a} C \Leftrightarrow B = C$

${2}^{13} = x$