Solve: (x-2)5^x = 5^(x+2)

Answer 1

(x-2)5^x - 5^(x+2) = 0
I see a common factor of 5^x
5^x( x-2 + 5^2) = 0
5^x(x + 23) = 0
5^x = 0 or x = -23

but 5^x = 0 has no solution, so

x = -23

Answer 2

take the log base 5 of each side.

log(x-2)+x =(x+2)

log(x-2)=2
log base five z=2, so x-2=25, x= 27

check it.
x-2)5^x = 5^(x+2)
25*5^25= 5^(27)
25= 5^2, checks.

Answer 3

go with bobpursley's solution

I don't know how my "-" suddenly turned into a + in my third line.

should have been:

5^x( x-2 - 5^2) = 0
5^x(x - 27) = 0
5^x = 0 or x = 27

but 5^x = 0 has no solution, so

x = 27 , the same as bob had