Solve the exponent equation :81^2x = 27^(4x-1).

The equation `81^(2x) = 27^(4x-1)` has to be
solved.

First equate the base of both sides of the
equation.

`81^(2x) =
27^(4x-1)`

`81 = 3^4` and `27 =
3^3`

This gives:

`(3^4)^(2x) =
(3^3)^(4x - 1)`

`3^(8x) = 3^(12x -
3)`

Now, the exponent terms of both the sides can be
equated to solve for x.

8x = 12x -
3

4x = 3

x =
3/4

The solution of the equation is x =
3/4.