SOLUTION: Can you please combine 4 ln sqrt x - ln (xy^5) + 3 ln y? Thank you.

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Question 322465: Can you please combine 4 ln sqrt x - ln (xy^5) + 3 ln y?
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4ln%28sqrt%28x%29%29-ln%28xy%5E5%29%2B3ln%28y%29 Start with the given expression.


4ln%28x%5E%281%2F2%29%5E%22%22%29-ln%28xy%5E5%29%2B3ln%28y%29 Convert to exponential notation.


ln%28x%5E%284%281%2F2%29%29%5E%22%22%29-ln%28xy%5E5%29%2Bln%28y%5E3%29 Use the identity y%2Aln%28x%29=ln%28x%5Ey%29


ln%28x%5E%284%2F2%29%5E%22%22%29-ln%28xy%5E5%29%2Bln%28y%5E3%29 Multiply


ln%28x%5E2%29-ln%28xy%5E5%29%2Bln%28y%5E3%29 Reduce.


ln%28%28x%5E2%29%2F%28xy%5E5%29%29%2Bln%28y%5E3%29 Combine the first two logs using the identity ln%28A%29-ln%28B%29=ln%28A%2FB%29


ln%28%28%28x%5E2%29%2F%28xy%5E5%29%29%28y%5E3%29%29 Combine the logs using the identity ln%28A%29%2Bln%28B%29=ln%28A%2AB%29


ln%28%28x%5E2y%5E3%29%2F%28xy%5E5%29%29 Combine the fractions.


ln%28x%2F%28y%5E2%29%29 Reduce.


So 4ln%28sqrt%28x%29%29-ln%28xy%5E5%29%2B3ln%28y%29=ln%28x%2F%28y%5E2%29%29