SOLUTION: 64^x=(1/16)

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Question 1026537: 64^x=(1/16)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
%288%5E2%29%5Ex=1%2F%282%5E4%29

%28%282%5E3%29%5E2%29%5Ex=2%5E%28-4%29

%282%5E6%29%5Ex=2%5E%28-4%29

2%5E%286x%29=2%5E%28-4%29

Bases are the same, so the exponents are equal.

6x=-4

x=-2%2F3

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

64^x=(1/16)
64%5Ex+=+1%2F16 -------> 64%5Ex+=+16%5E%28-+1%29

%284%5E3%29%5Ex+=+%284%5E2%29%5E-1

4%5E%283x%29+=+4%5E%28-+2%29

3x = - 2 ------- Bases are equal and so are their exponents

highlight_green%28x+=+-+2%2F3%29