SOLUTION: Please help me find where I made the mistake on an exponential equation. I tried to solve it and my result is 68=Y {{{1/64 = 4^y}}}

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Question 598308: Please help me find where I made the mistake on an exponential equation. I tried to solve it and my result is 68=Y
1%2F64+=+4%5Ey






Found 2 solutions by richard1234, jsmallt9:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
You're using the wrong arithmetic operation.

First note that 64 = 4^3 so 1/64 = 4^(-3). Therefore you have



So y = -3.

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F64+=+4%5Ey
One way to solve equations like this is, if possible, to write both sides of the equation as powers of the same number.

For this equation, you just have to figure out one of the following:
  • Is 4 a power of 64?
  • Is 64 a power of 4?
  • Are 4 and 64 both powers of some third number?

It is possible to say yes to all three of these questions. The easiest one is either the second or third. If you realize that 64+=+4%5E3, the solution is simple:
Rewrite the left side as a power of 4. Since 64+=+4%5E3, then 1%2F64+=+4%5E%28-3%29:
4%5E%28-3%29+=+4%5Ey
This equation says that two powers of 4 are equal. But this is only possible if the exponents are equal. So:
-3 = y
And we're finished!

FWIW, If it is not possible to write each side of the equation as powers of the same number, then logarithms must be used to solve the equation.