SOLUTION: write as a single logarithm log2 3+og2 y^5-3log2x

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Question 144421: write as a single logarithm
log2 3+og2 y^5-3log2x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%283%29%29%2Blog%282%2C%28y%5E5%29%29-3%2Alog%282%2C%282x%29%29 Start with the given expression


log%282%2C%283%29%29%2Blog%282%2C%28y%5E5%29%29-log%282%2C%28%282x%29%5E3%29%29 Rewrite 3%2Alog%282%2C%282x%29%29 as log%282%2C%28%282x%29%5E3%29%29 using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%282%2C%283%29%29%2Blog%282%2C%28y%5E5%29%29-log%282%2C%288x%5E3%29%29 Cube 2x to get 8x%5E3



log%282%2C%283y%5E5%29%29-log%282%2C%288x%5E3%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%282%2C%28%283y%5E5%29%2F%288x%5E3%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 log%282%2C%283%29%29%2Blog%282%2C%28y%5E5%29%29-3%2Alog%282%2C%282x%29%29 simplifies to log%282%2C%28%283y%5E5%29%2F%288x%5E3%29%29%29