SOLUTION: Write the expression as a single logarithm {{{log(b,(x-2))+3log(b,(x-6))-4log(b,(x+1))}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write the expression as a single logarithm {{{log(b,(x-2))+3log(b,(x-6))-4log(b,(x+1))}}}       Log On


   

Question 130685: Write the expression as a single logarithm


log%28b%2C%28x-2%29%29%2B3log%28b%2C%28x-6%29%29-4log%28b%2C%28x%2B1%29%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

log%28b%2C%28x-2%29%29%2B3log%28b%2C%28x-6%29%29-4log%28b%2C%28x%2B1%29%29 Start with the given expression


log%28b%2C%28x-2%29%29%2Blog%28b%2C%28x-6%29%5E3%29-log%28b%2C%28x%2B1%29%5E4%29 Rewrite the expression using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


log%28b%2C%28x-2%29%28x-6%29%5E3%29-log%28b%2C%28x%2B1%29%5E4%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%28b%2C%28x-2%29%28x-6%29%5E3%2F%28x%2B1%29%5E4%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