SOLUTION: what does it mean to express in terms of sums and defferences of logartithms? {{{log((sqrt(( x^2y)/z ))) }}}

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Question 84160: what does it mean to express in terms of sums and defferences of logartithms?
log%28%28sqrt%28%28+x%5E2y%29%2Fz+%29%29%29+

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

what does it mean to express in terms of sums 
and defferences of logartithms? 

log%28%28sqrt%28%28+x%5E2y%29%2Fz+%29%29%29+

Change the square root to the 1%2F2 power

log%28+%28%28x%5E2y%29%2Fz%29%5E%281%2F2%29+%29+

Now you can move the 1%2F2 power out in front
of the log, like this

%281%2F2%29log%28+%28%28x%5E2y%29%2Fz%29+%29+

Now the log of a QUOTIENT equals the log of the 
numerator MINUS the log of the denominator

%281%2F2%29%28log%28%28x%5E2y%29%29+-+log%28%28z%29%29%29

Now the log of a PRODUCT equals the log of the 
first factor x%5E2 PLUS the log of the second factor y.

%281%2F2%29%28log%28%28x%5E2%29%29+%2B+log%28%28y%29%29+-+log%28%28z%29%29%29

Now you can move the 2 power out in front
of the log, like this

%281%2F2%29%282%2Alog%28%28x%29%29+%2B+log%28%28y%29%29+-+log%28%28z%29%29%29

Now you can distribute the 1%2F2

log%28%28x%29%29+%2B+%281%2F2%29log%28%28y%29%29+-+%281%2F2%29log%28%28z%29%29

Edwin