SOLUTION: Hi, Can you tell me if I did the below right? Rewrite the following as a single logarithm: 7lnx+4lny-3lnz I had: =ln(x^7)Xy^4)(-z^3) Using property of natural log

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi, Can you tell me if I did the below right? Rewrite the following as a single logarithm: 7lnx+4lny-3lnz I had: =ln(x^7)Xy^4)(-z^3) Using property of natural log      Log On


   

Question 196051This question is from textbook Finite Math and Applied Calculus
: Hi,
Can you tell me if I did the below right?
Rewrite the following as a single logarithm:
7lnx+4lny-3lnz
I had:
=ln(x^7)Xy^4)(-z^3)
Using property of natural logs ln (m/n) - lnM-lnN
= ln (x^7y^4 / z^-3)
Please let me know. Thank you!! This question is from textbook Finite Math and Applied Calculus

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
7%2Aln%28x%29%2B4%2Aln%28y%29-3%2Aln%28z%29 Start with the given expression


ln%28x%5E7%29%2Bln%28y%5E4%29-ln%28z%5E3%29 Take the coefficients and place them as exponents (just the absolute value of the coefficients)


Note: y%2Aln%28x%29=ln%28x%5Ey%29


ln%28x%5E7%2Ay%5E4%29-ln%28z%5E3%29 Combine the logs using the identity ln%28A%29%2Bln%28B%29=ln%28AB%29


ln%28%28x%5E7%2Ay%5E4%29%2F%28z%5E3%29%29 Combine the logs using the identity ln%28A%29-ln%28B%29=ln%28A%2FB%29




So 7%2Aln%28x%29%2B4%2Aln%28y%29-3%2Aln%28z%29=ln%28%28x%5E7%2Ay%5E4%29%2F%28z%5E3%29%29 where x%3E=1, y%3E=1, and z%3E=1