Hey, how do I solve this? sqrt(x^(logsqrt(x)))=10

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Answer 1 · 2017-03-26T20:04:37

$x=e^(pm sqrt(4log(10)))$

$sqrt(x^(log(sqrt(x))))=10$ squaring

$x^(log(sqrt(x)))=10^2$

applying $log$ to both sides

$log(sqrt(x))log x = 2log10$ or

$1/2 (log x)^2=2log10$

then

$logx=pmsqrt(4log(10))$

and finally

$x=e^(pm sqrt(4log(10)))$

NOTE:

Adopting $log(x) equiv log_(10)x$ the result will be

$x = 10^(pm sqrt(4 log_10 10)) = 10^(pm 2) = {(0.01),(100):}$