## Algebra 2 (1st Edition)

$x = 8$
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 $x=8$