SOLUTION: how do you put this expression into single term? in(x2-9)-In(x-3)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: how do you put this expression into single term? in(x2-9)-In(x-3)      Log On


   

Question 1019268: how do you put this expression into single term? in(x2-9)-In(x-3)
Answer by ikleyn(52905) About Me  (Show Source):
You can put this solution on YOUR website!
.
how do you put this expression into single term? in(x2-9)-In(x-3)
------------------------------------------------------------------- 

1. ln%28x%5E2-9%29 - ln%28x-3%29 =       <-----  since  ln(a) - ln(b) = ln%28a%2Fb%29

   = ln%28%28x%5E2-9%29%2F%28x-3%29%29 =             <-----  x%5E2-9%29 = (x-3)*(x+3)

   = ln%28%28%28x-3%29%2A%28x%2B3%29%29%2F%28x-3%29%29 =        <-----  Now cancel (x-3) in numerator and denominator

   = ln%28%28cross%28%28x-3%29%29%2A%28x%2B3%29%29%2F%28cross%28x-3%29%29%29 =

   = ln(x+3).

2. Why do you write In and in for natural logarithm ?
    The standard symbol for natural logarithm is ln.