# How do you solve the equation log_2n=1/4log_2 16+1/2log_2 49?

Oct 30, 2016

$n = 14$

#### Explanation:

${\log}_{2} n = \frac{1}{4} {\log}_{2} 16 + \frac{1}{2} {\log}_{2} 49$

First use the log rule $a \log x = \log {x}^{a}$.

${\log}_{2} n = {\log}_{2} {16}^{\frac{1}{4}} + {\log}_{2} {49}^{\frac{1}{2}}$

${16}^{\frac{1}{4}} = \sqrt[4]{16} = 2$ and ${49}^{\frac{1}{2}} = \sqrt{49} = 7$

${\log}_{2} n = {\log}_{2} 2 + {\log}_{2} 7$

Use the log rule $\log x + \log y = \log x y$ to condense the log.

${\log}_{2} n = {\log}_{2} \left(2 \cdot 7\right)$

${\log}_{2} n = {\log}_{2} 14$

$n = 14$