SOLUTION: Hello! Use the Laws of Logarithms to combine the expression. log(x) + 1/4log(x^2+1)+5log(x-1) thanks for your help!

Algebra ->  Equations -> SOLUTION: Hello! Use the Laws of Logarithms to combine the expression. log(x) + 1/4log(x^2+1)+5log(x-1) thanks for your help!      Log On


   

Question 198952: Hello!
Use the Laws of Logarithms to combine the expression.
log(x) + 1/4log(x^2+1)+5log(x-1)
thanks for your help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C%28x%29%29%2B%281%2F4%29log%2810%2C%28x%5E2%2B1%29%29%2B5log%2810%2C%28x-1%29%29 Start with the given expression.


Rewrite the logs using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


Convert to radical notation.


log%2810%2C%28x%2Aroot%284%2Cx%5E2%2B1%29%2A%28x-1%29%5E5%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


So