4^(2x-5)=64^(3x) Solve the equation.

To evaluate the given equation 4^(2x-5)=64^(3x) , we may let 64 =4^3 .
The equation becomes:  4^(2x-5)=(4^3)^(3x) .
Apply Law of exponents: (x^n)^m = x^(n*m) .
4^(2x-5)=4^(3*3x)
4^(2x-5)=4^(9x)
Apply the theorem: If b^x=b^y then x=y .
If 4^(2x-5)=4^(9x ) then 2x-5=9x .
Subtract 2x on both sides of the equation 2x-5=9x .
2x-5-2x=9x-2x
-5=7x
Divide both sides by 7 .
(-5)/7=(7x)/7
x = -5/7
Checking: Plug-in x=-5/7 on 4^(2x-5)=64^(3x).
4^(2(-5/7)-5)=?64^(3*(-5/7))
4^((-10)/7-5)=?64^((-15)/7)
4^((-45)/7)=?64^((-15)/7)
4^((-45)/7)=?(4^3)^((-15)/7)
4^((-45)/7)=?4^(3*(-15)/7)
4^((-45)/7)=4^((-45)/7)  TRUE
or
0.000135~~0.000135  TRUE
Thus, the x=-5/7  is the real exact solution of the equation 4^(2x-5)=64^(3x) .