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):}#