5^(x-4)=25^(x-6) Solve the equation.

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 .