Question

Solve for x (2^2/x) (2^4/x) = 2^12

Answer 1

$\textsf{\qquad\qquad\huge\underline{{\sf Answer}}}$

Let's solve ~

$\qquad \sf \dashrightarrow \:(2 {}^{ \frac{2}{x} } ) \sdot(2 {}^{ \frac{4}{x} } ) = 2 {}^{12}$

$\qquad \sf \dashrightarrow \:(2 {}^{ \frac{2}{x} + \frac{4}{x} } ) = 2 {}^{12}$

$\qquad \sf \dashrightarrow \:(2 {}^{ \frac{6}{x} } ) = 2 {}^{12}$

Now, since the base on both sides are equal, therefore their exponents are equal as well ~

$\qquad \sf \dashrightarrow \: \dfrac{6}{x} = 12$

$\qquad \sf \dashrightarrow \:x = \dfrac{6}{12}$

$\qquad \sf \dashrightarrow \:x = \dfrac{1}{2}$

or

$\qquad \sf \dashrightarrow \:x = 0.5$

Hope you got the required Answer ~