SOLUTION: Hello! I am clueless where to go from here: Consider the following equation: ln(x+7) - ln(x-5)=ln x A. Solve the logarithmic equation algebraically X= B. Round your resu

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello! I am clueless where to go from here: Consider the following equation: ln(x+7) - ln(x-5)=ln x A. Solve the logarithmic equation algebraically X= B. Round your resu      Log On


   

Question 856194: Hello! I am clueless where to go from here:
Consider the following equation:
ln(x+7) - ln(x-5)=ln x
A. Solve the logarithmic equation algebraically
X=
B. Round your result to three decimal places
X=
This is what I have so far=
ln(x+7) - ln(x-5) - ln x= 0
ln(x+7)/x(x-5)=0
(x+7)/x(x-5)=1
x+7=x^2-5x
x^2-6x-7=0
Now I don't understand what to do. Can you please help me in understanding this equation?
Thank you so much!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You're almost there.
x%5E2-6x-7=0
%28x-7%29%28x%2B1%29=0
Two possible solutions:
x-7=0
x=7
Verify
ln%287%2B7%29-ln%287-5%29=ln%287%29
ln%2814%29-ln%282%29=ln%287%29
True
and
x%2B1=0
x=-1
Can't be a solution since ln%28-1%29 is not defined.
Only 1 solution, x=7