Answer
$x=8$
Work Step by Step
We know that $\log_a {x^n}=n\cdot \log_a {x}$, hence the equation $2\log_5{x}=3\log_5{4}$ becomes $\log_5{x^{2}}=\log_5{4^3}.$
RECALL:
$\log_a{b}=\log_a{c} \longrightarrow b=c$
Hence,
$\log_5{x^{2}}=\log_5{4^3}\longrightarrow x^{2}=4^3$
Solve the equation above to obtain \begin{align*} x^{2}&=4^3\\ x^{2}&=64 \\ \sqrt{x^{2}}&=\sqrt{64}\\ x &=8\end{align*}
(We only take the positive square root since $x$ must be greater than $0$.)
