SOLUTION: log(64)128

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Question 358333: log(64)128
Found 2 solutions by jsmallt9, edjones:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%2864%2C+%28128%29%29
The key to a simple solution to this is recognizing that both 64 and 128 are both powers of 2. So this expression will simplify quickly if we use the base conversion formula, log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29, to convert the base 64 logarithm into a base 2 logarithms:
log%2864%2C+%28128%29%29+=+log%282%2C+%28128%29%29%2Flog%282%2C+%2864%29%29
Since 2%5E6+=+64 and 2%5E7+=+128 the two logarithms are 6 and 7, respectively:
log%2864%2C+%28128%29%29+=+log%282%2C+%28128%29%29%2Flog%282%2C+%2864%29%29+=+7%2F6

If 64 and 128 were not both powers of the same number (or if we don't recognize that they are), then an expression like this can be simplified using the base conversion formula to change log%2864%2C+%28128%29%29 into logarithms your calculator "knows" (like base 10 or base e (aka ln)).

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
log(64)128=7/6