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

Question

asked Nov 18, 2023 72.4k views

1 Answer

Subchap · Answer 1 · 2023-11-23T15:41:04+0000

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

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 ~