3^(81x) = 81^(3x)
Let's do this by equating bases
Note 81 = 3^4 so we have
3^(81x) = [3^4]^(3x) simplify
3^(81x) = 3^(12x) since we have the bases the same, we can solve for the exponential equations
81x = 12x
81x - 12x = 0
(81 - 12)x = 0
69x = 0 and the only thing that makes this true is when x = 0