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22 November, 18:45

Solve '3^81^x=81^3^x' for x

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  1. 22 November, 18:52
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    The equation is

    3^81^x=81^3^x

    Taking the natural logarithim

    ln 3^81^x=ln 81^3^x

    Simplifying

    81^x ln 3 = 3^x ln 81

    Taking again the natural logarithim

    ln (81^x ln 3) = ln (3^x ln 81)

    Simplifying

    ln 81^x + ln (ln 3) = ln 3^x + ln (ln 81)

    x ln 81 + ln (ln 3) = x l n 3 + ln (ln 81)

    x ln 81 - x ln 3 = ln (ln 81) - ln (ln 3)

    x (ln 81/3) = ln (ln 81 / ln 3))

    x = ln (ln 81 / ln 3) / ln 27

    x ≈ 0.383
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