Verified answer

log(a) b = 1/log(b) a

a ^ log(a) b = b

log(a) b^k = k log(a) b

a^m*a^n = a^(m+n)

-------------------------

1/log(3)2 = log(2) 3

1/log(9) 2 = log(2) 9 = log(2) 3^2

.......

1/log(2187) 2 = log(2) 2187 = log(2) 3^7

⁷√( 2^(log(2) 3)*2^(log(2) 3^2)*2^(log(2) 3^3)*....*2^(log(2) 3^7)) =

= ⁷√(3*3²*3³*3⁴*3⁵*3⁶*3⁷) = ⁷√(3^(1+2+3+4+5+6+7) =

= ⁷√ 3^28 = ⁷√ (3^4)^7 = 3^4 = 81