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How to solve X^(5-log x^3)=100

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taking log10 of both sides,
(5-logx^3) logx = log100
(5 - 3logx)logx = 2
for ease of reading let u = logx, so we have
(5-3u)u = 2
3u^2 - 5u + 2 = 0
(3u-2)(u-1) = 0
u = 1 or 2/3

so, x = 10^1 = 10, or
x = 10^2/3 = ∛100

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