SOLUTION: Write as a single logarithm a) 1/2log(base y ) p^3 q^4 - 2/3log(base y) p^4 q^3 Can you please help me out? Thanks so much in advance:)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Write as a single logarithm a) 1/2log(base y ) p^3 q^4 - 2/3log(base y) p^4 q^3 Can you please help me out? Thanks so much in advance:)      Log On


   

Question 810572: Write as a single logarithm
a) 1/2log(base y ) p^3 q^4 - 2/3log(base y) p^4 q^3
Can you please help me out? Thanks so much in advance:)
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29log%28y%2C%28p%5E3q%5E4%29%29-%282%2F3%29log%28y%2C%28p%5E4q%5E3%29%29
The coefficients of the logs are exponents of the logs.
log%28y%2C%28p%5E3q%5E4%29%5E%281%2F2%29%29-log%28y%2C%28p%5E4q%5E3%29%5E%282%2F3%29%29
You can combine the logs because they have the same base.
Since you are subtracting you will use the division property.
log%28y%2C%28%28p%5E3q%5E4%29%5E%281%2F2%29%29%2F%28%28p%5E4q%5E3%29%5E%282%2F3%29%29%29
simplify
log%28y%2C%28%28p%5E%283%2F2%29q%5E2%29%2F%28p%5E%288%2F3%29q%5E2%29%29%29
log%28y%2C%28%281%29%2F%28p%5E%287%2F6%29%29%29%29
log%28y%2C%28%281%29%2F%28root%286%2Cp%5E7%29%29%29%29
log%28y%2C%28%281%29%2F%28p%2Aroot%286%2Cp%29%29%29%29
Rationalize
log%28y%2C%28%28root%286%2Cp%29%29%2F%28p%5E2%29%29%29
There is the final answer.