SOLUTION: express as a single logarithm log2x+5log2y−5log2z (that is log base two of x + 5 log base 2 o fx - 5 log base 2 of x)

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Question 541815: express as a single logarithm
log2x+5log2y−5log2z

(that is log base two of x + 5 log base 2 o fx - 5 log base 2 of x)

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

log%282%2C%28x%29%29%2B5%2Alog%282%2C%28y%29%29-5%2Alog%282%2C%28z%29%29

Use the rule that says we can move a coefficient of a log to the exponent of
what the log is taken of, which is written C%2Alog%28B%2C%28A%29%29 = log%28B%2C%28A%5EC%29%29

So

log%282%2C%28x%29%29%2B5%2Alog%282%2C%28y%29%29-log%282%2C%28z%29%29

becomes:

log%282%2C%28x%29%29%2Blog%282%2C%28y%5E5%29%29-log%282%2C%28z%5E5%29%29

On just the first two terms, we use the rule that says the sum of two logs is
the same as the log of the product of what the logs were taken of, which is
written log%28B%2C%28A%29%29 + log%28B%2C%28C%29%29 = log%28B%2C%28A%2AC%29%29

log%282%2C%28xy%5E5%29%29-log%282%2C%28z%5E5%29%29

Next we use the rule that says the difference of two logs is the same as the
log of the quotient of what the logs were taken of, which is written log%28B%2C%28A%29%29 - log%28B%2C%28C%29%29 = log%28B%2C%28A%2FC%29%29.

So the above becomes

log%282%2C%28xy%5E5%2Fz%5E5%29%29

Edwin