SOLUTION: I need to express log3x+6(logx-logy) as a single logarithm, and simplify if possible. I am not sure how to deal with the 6. This problem is from a handout, so there is no text info

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I need to express log3x+6(logx-logy) as a single logarithm, and simplify if possible. I am not sure how to deal with the 6. This problem is from a handout, so there is no text info      Log On


   

Question 85475: I need to express log3x+6(logx-logy) as a single logarithm, and simplify if possible. I am not sure how to deal with the 6. This problem is from a handout, so there is no text information.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C3x%29%2B6%2A%28log%2810%2C%28x%29%29-log%2810%2C%28y%29%29%29

log%2810%2C%283x%29%29%2B6%2A%28log%2810%2C%28x%2Fy%29%29%29 Combine the inner logs by using log%28b%2Cx%29-log%28b%2Cy%29=log%28b%2Cx%2Fy%29

log%2810%2C3x%29%2Blog%2810%2C%28x%2Fy%29%5E6%29 Use the identity a%2Alog%28b%2Cx%29=log%28b%2Cx%5Ea%29 to rewrite 6%2Alog%2810%2Cx%2Fy%29 into log%2810%2C%28x%2Fy%29%5E6%29

log%2810%2C3x%29%2Blog%2810%2C%28x%5E6%2Fy%5E6%29%29 Distribute the exponent

log%2810%2C3x%2A%28x%5E6%2Fy%5E6%29%29 Combine the logs using log%28b%2Cx%29%2Blog%28b%2Cy%29=log%28b%2Cx%2Ay%29

log%2810%2C%283x%5E7%2Fy%5E6%29%29 Multiply