SOLUTION: Write (log( 3, 7 ))(log( 4, 3 ))(log( 7, 6 )) as a single logarithm.

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Question 709692: Write (log( 3, 7 ))(log( 4, 3 ))(log( 7, 6 )) as a single logarithm.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28log%28+3%2C+%287+%29%29%29%28log%28+4%2C+%283+%29%29%29%28log%28+7%2C+%286+%29%29%29
The only way to combine logs is if they have the same base. So we will be working with the change of base formula, log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29, to match up the bases of the logarithms we've been given.

Seeing that the base of the first log matches the base of the 2nd log, I see good things happening if we start by changing the base of the first log from 7 to 4 (so it matches the base of the second log):

The base 4 logs of 3 cancel leaving:
%28log%28+4%2C+%287+%29%29%29%28log%28+7%2C+%286+%29%29%29
Again we have logs where the base of one is the same as the argument of the other. So I'll change the base of the second log from 7 to 4:
%28log%28+4%2C+%287+%29%29%29%28log%28+4%2C+%286+%29%29%2Flog%284%2C+%287%29%29%29
The base 4 logs of 7 cancel leaving:
log%28+4%2C+%286+%29%29