SOLUTION: Solve the logarithmic equation. Express your solutions in exact form only. In(3x+5)+In(3x-5)=6+In4

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the logarithmic equation. Express your solutions in exact form only. In(3x+5)+In(3x-5)=6+In4      Log On


   

Question 473030: Solve the logarithmic equation. Express your solutions in exact form only.
In(3x+5)+In(3x-5)=6+In4
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
ln%283x%2B5%29%2Bln%283x-5%29=6%2Bln4
system%283x%2B5%3E0%2C+3x-5%3E0%29 => system%283x%3E-5%2C++3x%3E5%29 => system%28x%3E-5%2F3%2C++x%3E5%2F3%29 => x%3E5%2F3
Let write 6 in the way 6=ln%28e%5E6%29
ln%283x%2B5%29%2Bln%283x-5%29=ln%28e%5E6%29%2Bln4
Use formula lna%2Blnb=ln%28ab%29
ln%28%283x%2B5%29%283x-5%29%29=ln%284e%5E6%29
%283x%2B5%29%283x-5%29=4e%5E6
Use formula %28a%2Bb%29%28a-b%29=a%5E2-b%5E2
9x%5E2-25=4e%5E6 add 25 to the both sides
9x%5E2=4e%5E6%2B25 divide by 9
x%5E2=%284e%5E6%2B25%29%2F9
x1=sqrt%28%284e%5E6%2B25%29%2F9%29
x2=-sqrt%28%284e%5E6%2B25%29%2F9%29%3C5%2F3extraneous root
Answer x=sqrt%28%284e%5E6%2B25%29%2F9%29