Question

Find the value of ${\log }_{4}32$.

Answer 1

Find the value

.Let ${\log }_{4}32=x$

$\Rightarrow 32=4^x$ $\left[\mathbf{\because }\mathbf{}\mathit{l}\mathit{o}{\mathit{g}}_{\mathbf{a}}\left(b\right)\mathbf{=}\mathit{x}\mathbf{}\mathbf{\Rightarrow }\mathbf{}\mathit{b}\mathbf{=}{\mathit{a}}^{\mathbf{x}}\right]$

$\Rightarrow 2^5=2^{2x}$

$\Rightarrow 2x=5$

$\Rightarrow x=\frac{5}{2}$

Hence, the required answer is $\frac{5}{2}$.