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

  • Math -

    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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