# How do you solve 4 Log_5 2 + Log_5 X = 3 Log_5 4 - Log_5 3?

$X = \frac{4}{3}$
$4 \cdot {\log}_{5} 2 + {\log}_{5} X = 3 \cdot {\log}_{5} 4 - {\log}_{5} 3$
${\log}_{5} {2}^{4} + {\log}_{5} X = {\log}_{5} {2}^{2 \cdot 3} - {\log}_{5} 3$
${\log}_{5} \left({2}^{4} \cdot X\right) = {\log}_{5} \left({2}^{6} / 3\right)$
${2}^{4.} X = {2}^{6} / 3$
$X = {2}^{6} / \left({2}^{4} \cdot 3\right) = {2}^{2} / 3 = \frac{4}{3}$