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 {}^{ (2)/(x) } ) \sdot(2 {}^{ (4)/(x) } ) = 2 {}^(12)`

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

`\qquad \sf  \dashrightarrow \:(2 {}^{ (6)/(x) } ) = 2 {}^(12)`

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

`\qquad \sf  \dashrightarrow \: (6)/(x) = 12`

`\qquad \sf  \dashrightarrow \:x = (6)/(12)`

`\qquad \sf  \dashrightarrow \:x = (1)/(2)`

or

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

Hope you got the required Answer ~