SOLUTION: Hello! I am unsure that this is the right topic to submit this question to, but I am pretty sure it is. (This problem is from a worksheet titled "Exponential and Logarithmic Fu

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello! I am unsure that this is the right topic to submit this question to, but I am pretty sure it is. (This problem is from a worksheet titled "Exponential and Logarithmic Fu      Log On


   

Question 723566: Hello!
I am unsure that this is the right topic to submit this question to, but I am pretty sure it is. (This problem is from a worksheet titled "Exponential and Logarithmic Functions".)
We have gone over all of the basic concepts, and I understand them very well. However, I am very unsure of how to go about this particular problem.
1/2[log4(x+1)+2log4(x-1)]+6log4x

I honestly don't know where to start.
Thank you so much!
--Mandy
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F2%28log%284%2C%28x%2B1%29%29%2B2log%284%2C%28x-1%29%29%29 + 6log%284%2Cx%29
Multiply inside the brackets by 1/2, gets rid of the 2
1%2F2log%284%2C%28x%2B1%29%29%2Blog%284%2C%28x-1%29%29 + log%284%2Cx%5E6%29
log%284%2C%28x%2B1%29%5E%281%2F2%29%29%2Blog%284%2C%28x-1%29%29 + log%284%2Cx%5E6%29
an exponent of 1/2 is the square root
log%284%2C%28sqrt%28x%2B1%29%29%29%2Blog%284%2C%28x-1%29%29 + log%284%2Cx%5E6%29
can be written
log%284%2C%28sqrt%28x%2B1%29%29%2A%28x-1%29%2A%28x%5E6%29%29
log%284%2C%28sqrt%28x%2B1%29%29%2A%28x%5E7-x%5E6%29%29