SOLUTION: Solve the equation. Find the exact solution if possible; otherwise, use a calculator to approximate to four decimals. {{{2log (3,x)-log(3,(x-4))=2+log(3,2) }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the equation. Find the exact solution if possible; otherwise, use a calculator to approximate to four decimals. {{{2log (3,x)-log(3,(x-4))=2+log(3,2) }}}       Log On


   

Question 805114: Solve the equation. Find the exact solution if possible; otherwise, use a calculator to approximate to four decimals.
2log+%283%2Cx%29-log%283%2C%28x-4%29%29=2%2Blog%283%2C2%29++
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
2log+%283%2Cx%29-log%283%2C%28x-4%29%29=2%2Blog%283%2C2%29++

Isolate the logs on whichever side will cause the most logs to be
positive:


                     -2=log+%283%2C2%29%2Blog%283%2C%28x-4%29%29-2log+%283%2Cx%29
                     -2=log+%283%2C2%28x-4%29%29-2log+%283%2Cx%29
                     -2=log+%283%2C2%28x-4%29%29-log+%283%2Cx%5E2%29
                     -2=log%283%2C2%28x-4%29%2Fx%5E2%29
                     3%5E%28-2%29=2%28x-4%29%2Fx%5E2
                     1%2F3%5E2=2%28x-4%29%2Fx%5E2
                     1%2F9=2%28x-4%29%2Fx%5E2
                     x%5E2=18%28x-4%29
                     x%5E2=18x-72
                     x%5E2-18x%2B72=0
                     %28x-6%29%28x-12%29=0
                     x-6=0;  x-12=0
                       x=6;     x=12

Neither answer causes the original problem to take the
log of a negative number.  So those are the solutions.

If you have any questions, ask them in the thank-you note 
and I'll get back to you.

Edwin