SOLUTION: Express as a single logarithm: 5logex+logey-2logez All the e"s are subscript. Thank you.

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Question 169152: Express as a single logarithm:
5logex+logey-2logez
All the e"s are subscript.
Thank you.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
5%2Alog%28e%2C%28x%29%29%2Blog%28e%2C%28y%29%29-2%2Alog%28e%2C%28z%29%29 Start with the given expression


log%28e%2C%28x%5E5%29%29%2Blog%28e%2C%28y%29%29-log%28e%2C%28z%5E2%29%29 Rewrite the expression using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29. In other words, place the coefficients as exponents.


log%28e%2C%28x%5E5y%29%29-log%28e%2C%28z%5E2%29%29 Combine the first two logs using the identity log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29


log%28e%2C%28%28x%5E5y%29%2F%28z%5E2%29%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


So 5%2Alog%28e%2C%28x%29%29%2Blog%28e%2C%28y%29%29-2%2Alog%28e%2C%28z%29%29 simplifies to log%28e%2C%28%28x%5E5y%29%2F%28z%5E2%29%29%29