SOLUTION: Express as a single logarithm 1/2 Log a X + 3 Log a Y - 2 Log a X

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Question 198851: Express as a single logarithm
1/2 Log a X + 3 Log a Y - 2 Log a X

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29log%28a%2C%28x%29%29%2B3%2Alog%28a%2C%28y%29%29-2%2Alog%28a%2C%28x%29%29 Start with the given expression.


log%28a%2C%28x%5E%281%2F2%29%29%29%2Blog%28a%2C%28y%5E3%29%29-log%28a%2C%28x%5E2%29%29 Rewrite the logs using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%28a%2C%28sqrt%28x%29%29%29%2Blog%28a%2C%28y%5E3%29%29-log%28a%2C%28x%5E2%29%29 Convert to radical notation.


log%28a%2C%28sqrt%28x%29%2Ay%5E3%29%29-log%28a%2C%28x%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%28a%2C%28%28sqrt%28x%29%2Ay%5E3%29%2F%28x%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