Solve 3^(x-2)-9=0.

Since we have 3^(x-2), we'll apply the quotient
rule:

a^(b-c) = a^b/a^c

We'll put 3 =
2, b = x and c = 2

3^(x-2) =
3^x/3^2

But 3^2  = 9

3^(x-2) =
3^x/9

We'll re-write the
equation:

3^x/9  -  9 = 0

We'll
multiply by 9 both sides:

3^x - 81 =
0

We'll add 81 both sides:

3^x =
81

We'll write 81 as a power of 3:

81 =
3^4

3^x = 3^4

Since the bases are
matching, we'll apply one to one property:

x =
4