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
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