SOLUTION: How can I write the expression as a logarithm of a single quantity for the following exercise. 1/2ln(x)+4ln(y)-3ln(z) Thanks, Leidy

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: How can I write the expression as a logarithm of a single quantity for the following exercise. 1/2ln(x)+4ln(y)-3ln(z) Thanks, Leidy      Log On


   

Question 272850: How can I write the expression as a logarithm of a single quantity for the following exercise.
1/2ln(x)+4ln(y)-3ln(z)
Thanks,
Leidy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29%2Aln%28x%29%2B4%2Aln%28y%29-3%2Aln%28z%29 Start with the given expression.


ln%28x%5E%281%2F2%29%5E%22%22%29%2Bln%28y%5E4%29-ln%28z%5E3%29 Use the identity y%2Aln%28x%29=ln%28x%5Ey%29


ln%28sqrt%28x%29%29%2Bln%28y%5E4%29-ln%28z%5E3%29 Convert to radical notation.


ln%28sqrt%28x%29%2Ay%5E4%29-ln%28z%5E3%29 Combine the first two logs using the identity ln%28x%29%2Bln%28y%29=ln%28xy%29


ln%28y%5E4%2Asqrt%28x%29%29-ln%28z%5E3%29 Rearrange the terms.


ln%28%28y%5E4%2Asqrt%28x%29%29%2Fz%5E3%29 Combine the logs using the identity ln%28x%29-ln%28y%29=ln%28x%2Fy%29


So where each variable is greater than zero.