Answer
$x = 8$
Work Step by Step
Since $25 = 5^2$ we can multiply the exponent of the left hand side by $2$ while reducing the base to $5$.
The new equation is $5^{x-4}= 5^{2(x-6)}$.
Distributing the $2$ gives,
$5^{x-4}= 5^{2x-12}$
We can now use Key Concept Algebra on pg. 515 stating if b is a positive number other than 1, then $b^x $ $= b^y$
if and only
if $x = y$.
Thus $ x -4 = 2x-12$
After moving the variables to one side and the constants to the other,
$ 8 = x $ or $x=8$
