SOLUTION: What's the solution for log64 1/4=x?

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Question 630651: What's the solution for log64 1/4=x?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%2864%2C+%281%2F4%29%29+=+x
The key here is to notice that both 64 and 1/4 are powers of 4: 64+=+4%5E3 and 1%2F4+=+4%5E%28%28-1%29%29. So this expression will simplify quickly if we change the base to 4.

The change of base formula is
log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29
Using this on our expression, to change the base from 64 to 4, we get:
log%284%2C+%281%2F4%29%29%2Flog%284%2C+%2864%29%29+=+x
Since we know what powers of 4 64 and 1/4 are, we can substitute in for those logs:
%28-1%29%2F3+=+x
And we're finished!