SOLUTION: PLEASE HELP ME WITH THIS PROBLEM; solve the equation In(x+5)- In(3)= In (x-3)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: PLEASE HELP ME WITH THIS PROBLEM; solve the equation In(x+5)- In(3)= In (x-3)      Log On


   

Question 54934: PLEASE HELP ME WITH THIS PROBLEM;
solve the equation In(x+5)- In(3)= In (x-3)
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The rules we're going to use are:
1.highlight%28ln%28a%29-ln%28b%29=ln%28a%2Fb%29%29
2. highlight%28ln%28a%29=b%29=>highlight%28a=e%5Eb%29
3. highlight%28a%5E0=1%29
solve the equation ln(x+5)- ln(3)= ln (x-3)
ln%28x%2B5%29-ln%283%29-ln%28x-3%29=ln%28x-3%29-ln%28x-3%29
ln%28x%2B5%29-ln%283%29-ln%28x-3%29=0
ln%28%28x%2B5%29%2F%283%28x-3%29%29%29=0 Rule 1
%28x%2B5%29%2F%283%28x-3%29%29=e%5E0 Rule 2
%28x%2B5%29%2F%283%28x-3%29%29=1 Rule 3
3%28x-3%29%28x%2B5%29%2F%283%28x-3%29%29=3%28x-3%29%281%29
cross%283%28x-3%29%29%28x%2B5%29%2Fcross%283%28x-3%29%29=3%28x-3%29
x%2B5=3x-9
-x%2Bx%2B5=-x%2B3x-9
5=2x-9
9%2B5=2x-9%2B9
14=2x
14%2F2=2x%2F2
7=x
:
Check by subtituting 7 in for x's in the original equation and see if both sides equal once you simplify:
ln%287%2B5%29-ln%283%29=ln%287-3%29
ln%2812%29-ln%283%29=ln%284%29
ln%2812%2F3%29=ln%284%29 Rule 1
ln%284%29=ln%284%29 We're right!!!
Happy Calculating!!!