SOLUTION: express the following as a single logarithm: 1/4loga(x) – 3loga(y) – 2loga(z) Note: the a's are subscripts I am homeschooling my 9th grade son; this problem is on a test,

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: express the following as a single logarithm: 1/4loga(x) – 3loga(y) – 2loga(z) Note: the a's are subscripts I am homeschooling my 9th grade son; this problem is on a test,      Log On


   

Question 135059: express the following as a single logarithm:
1/4loga(x) – 3loga(y) – 2loga(z)
Note: the a's are subscripts
I am homeschooling my 9th grade son; this problem is on a test, and we are questioning the solution given.
Thanks, Beth.
Found 2 solutions by solver91311, vleith:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You need two logarithm rules and one exponent rule to do this one:

Exponent rule: x%5E%281%2Fn%29=root%28n%2Cx%29

Log rule 1: n%2Alog%28a%2Cx%29=log%28a%2Cx%5En%29

Log rule 2: log%28a%2Cx%29-log%28a%2Cy%29=log%28a%2C%28x%2Fy%29%29

%281%2F4%29log%28a%2Cx%29-3%2Alog%28a%2Cy%29-2%2Alog%28a%2Cz%29

log%28a%2C%28root%284%2Cx%29%29%29-log%28a%2C%28y%5E3%29%29-log%28a%2C%28z%5E2%29%29

log%28a%2C%28%28root%284%2Cx%29%29%2F%28y%5E3z%5E2%29%29%29 or log%28a%2C%28%28x%5E%281%2F4%29%29%2F%28y%5E3z%5E2%29%29%29 depending on your book's notation convention.

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Beth, i don' claim to be a guru at logs, but here is what I get. Compare that to your book and please let me know what it says .
+%281%2F4%29Logax+-+3Logay+-+2Logaz+
+Logax%5E%281%2F4%29+-+Logay%5E3+-+Logaz%5E2+
+Logax%5E%281%2F4%29+-+%28Logay%5E3+%2B+Logaz%5E2%29+
+Logax%5E%281%2F4%29+-+Loga%28y%5E3z%5E2%29+
+Loga%28x%5E%281%2F4%29%2F%28y%5E3z%5E2%29%29+
Does that agree with your book?