SOLUTION: Hello! Use the Laws of Logarithms to combine the expression -4log(4)(A)+3log(4)(B)+3log(4)(C) (4) is the base. thanks for your help!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello! Use the Laws of Logarithms to combine the expression -4log(4)(A)+3log(4)(B)+3log(4)(C) (4) is the base. thanks for your help!      Log On


   

Question 198957: Hello!
Use the Laws of Logarithms to combine the expression
-4log(4)(A)+3log(4)(B)+3log(4)(C)
(4) is the base.
thanks for your help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-4%2Alog%284%2C%28A%29%29%2B3%2Alog%284%2C%28B%29%29%2B3%2Alog%284%2C%28C%29%29 Start with the given expression.


-log%284%2C%28A%5E4%29%29%2Blog%284%2C%28B%5E3%29%29%2Blog%284%2C%28C%5E3%29%29 Rewrite the logs using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%284%2C%28B%5E3%29%29%2Blog%284%2C%28C%5E3%29%29-log%284%2C%28A%5E4%29%29 Rearrange the terms.


log%284%2C%28B%5E3%2AC%5E3%29%29-log%284%2C%28A%5E4%29%29 Combine the logs using the identity log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29


log%284%2C%28%28B%5E3%2AC%5E3%29%2F%28A%5E4%29%29%29 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


So