SOLUTION: Can you please help me to write this logarithm as a single logarithm? 1/2logx + 1/3logy -2logz Thank you!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Can you please help me to write this logarithm as a single logarithm? 1/2logx + 1/3logy -2logz Thank you!      Log On


   

Question 404296: Can you please help me to write this logarithm as a single logarithm?
1/2logx + 1/3logy -2logz
Thank you!
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
write this logarithm as a single logarithm?
1/2logx + 1/3logy -2logz
===
= log[x^(1/2)*y^(1/3)/z^(2)]
==============
Cheers,
Stan H.
==============

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29logx+%2B+%281%2F3%29logy+-2logz


use power rule:
a+log+b+=+log+a%5Eb


%281%2F2%29logx+=+log+x%5E%281%2F2%29

%281%2F3%29logy+=+log+y%5E%281%2F3%29
-2logz+=+log+z%5E%28-2%29

The the addition rule:

And remember for powers:

x%5E%281%2F2%29=+sqrt%28x%29
y%5E%281%2F3%29=root%283%2Cy%29
z%5E%28-2%29=1%2Fz%5E2

so, you will have: