SOLUTION: how do you condense the following logarithms? I'm confused and need help. 3 log3X + 4 log3Y-4log3Z and 2[3 ln x-ln(x+1)-ln(x-1)]

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: how do you condense the following logarithms? I'm confused and need help. 3 log3X + 4 log3Y-4log3Z and 2[3 ln x-ln(x+1)-ln(x-1)]      Log On


   

Question 244644: how do you condense the following logarithms? I'm confused and need help.
3 log3X + 4 log3Y-4log3Z
and
2[3 ln x-ln(x+1)-ln(x-1)]
Found 2 solutions by JimboP1977, solver91311:
Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
Log Rules that you should learn:
1) logb%28mn%29+=+logb%28m%29+%2B+logb%28n%29
2) logb%28m%2Fn%29+=+logb%28m%29+%96+logb%28n%29
3) logb%28m%5En%29+=+n+%B7+logb%28m%29


Assuming log3 means log(base 3):
3+log3X+%2B+4+log3Y-4log3Z+
log3x%5E3%2Blog3Y%5E4-log3Z%5E4 Using rule 3
log3+%28x%5E3%2Ay%5E4%29%2Fz%5E4 Using rule 1 and 2
2%283+ln+x-ln%28x%2B1%29-ln%28x-1%29%29
2%28+ln+x%5E3-ln%28x%2B1%29-ln%28x-1%29%29 Using rule 3
2%28+ln+%28%28x%5E3%2F%28x%2B1%29%29%2F%28x-1%29%29%29 Using rule 2
ln+%28x%5E3%2F%28%28x%2B1%29%2A%28x-1%29%29%29%5E2 Using rule 3
ln+%28x%5E6%2F%28%28x%2B1%29%5E2%2A%28x-1%29%5E2%29%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




First use:



to write:



Then use the fact that the sum of the logs is the log of the product, that is:



to write:



Then use the fact that the difference of the logs is the log of the quotient, that is:



To write:



and you are done.



Distribute the 2:



Then continue in the same fashion as illustrated in the first problem to finish the second one.

John