Question

3^(x-5)=9

x=2
x=-3
x=7
x=8

Answer 1

If you agree that 3^2 = 9 then we can also right it this way
3^(x-5) = 3^2
that means that x-5 = 2, so x = 7

Answer 2

Create equivalent expressions in the equation that all have equal bases.
3^(x-5)=3^(2)

Since the bases are the same, then two expressions are only equal if the exponents are also equal.
(x-5)=2

Since -5 does not contain the variable to solve for, move it to the other side of the equation
x=5+2

Add 2 to 5 to get7
x=7