SOLUTION: 1.)Solve the equation 2^(2x � 1) = 8^(x + 7). 2.)Solve the equation 3^x = 3^(3x + 1). 3.)Solve the equation (1/3)^x = 3^(x � 6). I just can't figure these out. Thanks so much

Question 558011: 1.)Solve the equation 2^(2x � 1) = 8^(x + 7).
2.)Solve the equation 3^x = 3^(3x + 1).
3.)Solve the equation (1/3)^x = 3^(x � 6).
I just can't figure these out. Thanks so much for helping!!!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
1.)
Since , substituting in the equation given, we get
and applying the properties of exponents, that simplifies to
, which simplifies further to

Since both sides are powers of the same base (2), the exponents must be equal, so we solve
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Checking: and
2.)
Since both sides are powers of the same base (3), the exponents must be equal, so we solve
--> --> -->
3.)
, so we can write the equation as
and applying the properties of exponents, that simplifies to

Since both sides are powers of the same base (3), the exponents must be equal, so we solve
--> --> --> --> -->
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