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Solve 1/4 x ^(log(2)sqrtx)=(2*x^(log(2)x...

Solve `1/4 x ^(log_(2)sqrtx)=(2*x^(log_(2)x))^(1/4).`

Text Solution

Verified by Experts

Taking log on both sides with base 2, we get
` log_(2)(1/4)+(log_(2)sqrtx)(log_(2)x)=1/4+1/4(log_(2)x)^(2)`
` or (log_(2)x)^(2) = 9 or log_(2)x = pm3`
` :. x = 8 or 1/8`
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