[256] If log_{4}x+log_{2}x=12, then x is equal to:

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If $log_{4}x+log_{2}x$=12, then x is equal to:

1024

256

Explanation:

$log_{4}x+log_{2}x$=12

=>$\dfrac{log\:x}{log\:4}+\dfrac{log\:x}{log\:2}$=12

=>$\dfrac{log\:x}{log\:2^2}+\dfrac{log\:x}{log\:2}$=12

=>$\dfrac{log\:x}{2\:log\:2}+\dfrac{log\:x}{log\:2}$=12

=>$\dfrac{log\:x+2\:log\:x}{2\:log\:2}$=12

=>$\dfrac{3\:log\:x}{2\:log\:2}$=12

Therefore,

logx=$\dfrac{12\times2\:log\:2}{3}$

=8 log 2

=$log(2^8)$

=log(256)

x=256

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