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

Solve For X 22x 24x 212 class=

Sagot :

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[tex] \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} } ) \sdot(2 {}^{ \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} + \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{6}{x} } ) = 2 {}^{12} [/tex]

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

[tex]\qquad \sf  \dashrightarrow \: \dfrac{6}{x} = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{6}{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{1}{2} [/tex]

or

[tex]\qquad \sf  \dashrightarrow \:x = 0.5[/tex]

Hope you got the required Answer ~

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