x^(log10x)=100

Question

I'm not sure how to do this at all...

Answer 1

I will assume you meant ...

x^(log₁₀ x = 100

then by definition:

log_x 100 = log₁₀x
changing to a common base of the log ...

log₁₀ 100/log_x = log_x/log₁₀10
2/log₁₀x = log₁₀ x/1
(log₁₀ x)^2 = 2
log₁₀ x =√2

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

(both answers can be verified)