Asked by Tyler

x^(log10x)=100

I'm not sure how to do this at all...
Answered by Reiny
I will assume you meant ...

x^(log<sub>10</sub> x = 100

then by definition:

log<sub>x</sub> 100 = log<sub>10</sub>x
changing to a common base of the log ...

log<sub>10</sub> 100/log<sub>x</sub> = log<sub>x</sub>/log<sub>10</sub>10
2/log<sub>10</sub>x = log<sub>10</sub> x/1
(log<sub>10</sub> x)^2 = 2
log<sub>10</sub> x =√2

using my calculator
x = appr 25.9546 or x = appr .03853

(both answers can be verified)
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