`5^(x-4)=25^(x-6)`

To solve, factor the 25.

`5^(x-4)=(5^2)^(x-6)`

To simplify the right side, apply the exponent rule `(a^m)^n = a^(m*n)` .

`5^(x-4)=5^(2*(x-6))`

`5^(x-4)=5^(2x-12)`

Since both sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right.

`x-4=2x-12`

`x-2x=4-12`

`-x=-8`

`x=8`

Therefore, the solution is `x=8` .