Friday, February 8, 2013

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

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