SOLUTION: Can you please explain how to this works out: {{{log(2,X)}}},{{{log(4,X)}}}

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Question 4988: Can you please explain how to this works out: log%282%2CX%29,log%284%2CX%29
Answer by ichudov(499) About Me  (Show Source):
You can put this solution on YOUR website!
Sure, say X+=+4%5EY that means that Y=log%28+4%2C+X+%29
X+=+4%5EY+=+%282%2A2%29%5EY+=+2%5EY%2A2%5EY
X+=+2%5EY%2A2%5EY
take a log with base 2 of the right part of the formula above
log%28+2%2C+X+%29+=+log%28+2%2C+2%5EY%2A2%2AY%29+%0D%0A=+log%28+2%2C+2%5EY%29+%2B+log%28+2%2C+2%5EY%29+%0D%0A=+2%2Alog%28+2%2C+2%5EY+%29
Since log%28+2%2C+2%5EY+%29 is Y, we have
log%28+2%2C+X+%29+=+2Y
Y, as we know is log%28+4%2C+X+%29, so
log%28+2%2C+X+%29+=+2%2Alog%28+4%2C+X+%29