SOLUTION: Write logarithm as a Sum or Difference Log has no base {{{log((x^3)sqrt(x+1)/(x-2)^2)}}} {{{3log(x)+ (1/2)log(x+1)-2log(x-2)}}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Write logarithm as a Sum or Difference Log has no base {{{log((x^3)sqrt(x+1)/(x-2)^2)}}} {{{3log(x)+ (1/2)log(x+1)-2log(x-2)}}}      Log On


   

Question 930331: Write logarithm as a Sum or Difference Log has no base
log%28%28x%5E3%29sqrt%28x%2B1%29%2F%28x-2%29%5E2%29
3log%28x%29%2B+%281%2F2%29log%28x%2B1%29-2log%28x-2%29
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28x%5E3%2Asqrt%28x%2B1%29%2F%28x-2%29%5E2%29%29

First use the rule: log%28%28A%2FB%29%29=log%28A%29-log%28B%29 with A=x%5E3%2Asqrt%28x%2B1%29 and B=%28x-2%29%5E2.  So we have:

log%28%28x%5E3%2Asqrt%28x%2B1%29%29-log%28%28%28x-2%29%5E2%29%29%29

Use the rule log%28A%2AB%29=log%28A%29%2Blog%28B%29 on the first term with A=x%5E3 and B=sqrt%28x%2B1%29

log%28%28x%5E3%29%29%2Blog%28%28sqrt%28x%2B1%29%29%29-log%28%28x-2%29%5E2%29%29



log%28%28x%5E3%29%29%2Blog%28%28x%2B1%29%5E%281%2F2%29%29-log%28%28x-2%29%5E2%29%29

Use the rule log%28%28A%5EB%29%29=B%2Alog%28%28A%29%29 on all three terms:

3%2Alog%28%28x%29%29%2Bexpr%281%2F2%29%2Alog%28%28x%2B1%29%29-2%2Alog%28%28x-2%29%29%29

Edwin