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
