Question

Find the value of n ${\left(\sqrt[4]{46}\right)}^n=36\sqrt{6}$

Answer 1

Given that

$6^{n/4}=36\sqrt{6}$

$\Rightarrow 6^{n/4}=6^2\times 6^{1/2}$

$\Rightarrow 6^{n/4}=6^{5/2}$

Bases on both sides of equality are equal. Hence, exponents can be equated.

$\Rightarrow \frac{n}{4}=\frac{5}{2}$

$\Rightarrow n=\frac{5}{2}\times 4$

$\Rightarrow n=10$