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

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