SOLUTION: Solve the equation (1/3)^x=27

Question 47129: Solve the equation
(1/3)^x=27
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
(1/3)^x=27
3^-x=27 [Convert the left side to a negative exponent (-x)]
3^-x=3^3 [convert to similar bases]
.
.
The following operations are performed within the exponents only:
3^(-x-3) = 3^3-3 [Solve for "x" within the exponents]
3^(-x-3=0) = 3^(3-3) [Answer within the exponents]
3^(x=-3) = 3^(3-3=0) [Answer within the exponents: solve for "x"]
3^-3 = 3^0 [Answer within the exponents]
.
..
Returning to the entire original equation
1/3^-3 =3^3 [Plug-in x=-3 into the original equation]
3^3 =3^3
27=27 [Checks out]

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