SOLUTION: Simplify: Log(base 4)64^x

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Question 614702: Simplify: Log(base 4)64^x
Found 2 solutions by nerdybill, MathTherapy:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify: Log(base 4)64^x
.
log%284%2C64%29
log%284%2C4%5E3%29
3

Answer by MathTherapy(10809) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify: Log(base 4)64^x

If log+%284%2C+%2864%5Ex%29%29, then read on!!
log+%284%2C+%284%5E3%29%5Ex%29
log+%284%2C+%284%5E%283x%29%29%29
       3x ----- Applying log+%28a%2C+%28a%5Eb%29%29 = b
OR

Let simplified form, be t
log+%284%2C+%2864%5Ex%29%29
4%5Et+=+64%5Ex ----- Converting to EXPONENTIAL form
4%5Et+=+%284%5E3%29%5Ex 
4%5Et+=+4%5E%283x%29
Exponents are equal, if BASES are equal, and so, simplified form, or t = 3x