SOLUTION: Express 3log b x-4 log b y+1/2 log b z as a single logarithm and simplify if possible. I am at a total loss. Please help... Thank you very much in advance!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Express 3log b x-4 log b y+1/2 log b z as a single logarithm and simplify if possible. I am at a total loss. Please help... Thank you very much in advance!      Log On


   

Question 152980: Express 3log b x-4 log b y+1/2 log b z as a single logarithm and simplify if possible. I am at a total loss. Please help... Thank you very much in advance!
Found 2 solutions by vleith, Fombitz:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Alogb%28x%29+-+4%2Alogb%28y%29+%2B+1%2F2%2Alogb%28z%29
See this page for the 'rules' about logs --> http://www.mathwords.com/l/logarithm_rules.htm

We will use rule 4 first
3%2Alogb%28x%29+-+4%2Alogb%28y%29+%2B+1%2F2%2Alogb%28z%29
logb%28x%5E3%29+-+logb%28y%5E4%29+%2B+logb%28z%5E%281%2F2%29%29
Now use rule 3
logb%28x%5E3%29+-+logb%28y%5E4%29+%2B+logb%28z%5E%281%2F2%29%29
logb%28x%5E3%2Fy%5E4%29+%2B+logb%28z%5E%281%2F2%29%29
Now use rule 2
logb%28x%5E3%2Fy%5E4%29+%2B+logb%28z%5E%281%2F2%29%29
logb%28%28x%5E3+%2A+z%5E%281%2F2%29%29+%2Fy%5E4%29+

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Three rules to use here.
log%28b%2CX%29%2Blog%28b%2CY%29=log%28b%2CXY%29
log%28b%2CX%29-log%28b%2CY%29=log%28b%2C%28X%2FY%29%29
a%2Alog%28b%2CZ%29=log%28b%2CZ%5Ea%29
I'm not sure of your equation but here's what I think it is,
1.3%2Alog%28b%2Cx%29-4%2Alog%28b%2Cy%29%2B%281%2F2%29log%28b%2Cz%29
although it might be,
2.3%2Alog%28b%2C%28x-4%29%29-log%28b%2Cy%29%2B%281%2F2%29log%28b%2Cz%29
Let's look at each term separately, then we'll put it all together.
3%2Alog%28b%2Cx%29=log%28b%2Cx%5E3%29
4%2Alog%28b%2Cy%29=log%28b%2Cy%5E4%29
%281%2F2%29log%28b%2Cz%29=log%28b%2Cz%5E%281%2F2%29%29



If it's eq. 2, then the solution becomes,