SOLUTION: Simplify into a single logarithm: log3 x-4log3y (both the 3's are below the g itself)

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Question 164881: Simplify into a single logarithm:
log3 x-4log3y (both the 3's are below the g itself)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C%28x%29%29-4log%283%2C%283y%29%29 Start with the given expression


log%283%2C%28x%29%29-log%283%2C%28%283y%29%5E4%29%29 Rewrite the second logarithm using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%283%2C%28%28x%29%2F%283y%29%5E4%29%29 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


log%283%2C%28%28x%29%2F%2881y%5E4%29%29%29 Expand and simplify


So log%283%2C%28x%29%29-4log%283%2C%283y%29%29 simplifies to log%283%2C%28%28x%29%2F%2881y%5E4%29%29%29