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worty [1.4K]
1 year ago
14

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

Mathematics
1 answer:
earnstyle [38]1 year ago
8 0

\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 ~

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