Solve the equation: $\;$ $\log_4 2^{4x} = 2^{\log_2 4}$
Given equation: $\;\;$ $\log_4 2^{4x} = 2^{\log_2 4}$
i.e. $\;$ $4x \log_4 2 = 4$ $\;\;\;$ $\left[\because \;\; \log_a m^n = n \log_a m; \;\;\; a^{\log_a m} = m\right]$
i.e. $\;$ $x \log_4 4^{\frac{1}{2}} = 1$
i.e. $\;$ $\left(\dfrac{x}{2}\right) \log_4 4 = 1$
i.e. $\;$ $\dfrac{x}{2} = 1$ $\implies$ $x = 2$
$\therefore \;$ The solution to the given equation is $\;\;$ $x = \left\{2 \right\}$