SOLUTION: How do you find the exact solution(s) to this problem? {{{ ln(2x+1) + ln(x-3) - 2 ln(x) = 0 }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do you find the exact solution(s) to this problem? {{{ ln(2x+1) + ln(x-3) - 2 ln(x) = 0 }}}      Log On


   

Question 1001179: How do you find the exact solution(s) to this problem?
+ln%282x%2B1%29+%2B+ln%28x-3%29+-+2+ln%28x%29+=+0+
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
+ln%282x%2B1%29+%2B+ln%28x-3%29+-+2+ln%28x%29+=+0+

+ln%28%282x%2B1%29%28x-3%29%5E%22%22%29+-+ln%28x%5E2%29+=+0+

+ln%28%282x%2B1%29%28x-3%29%5E%22%22%29+=+ln%28x%5E2%29+

Since this shows the equality of two natural
logarithms, we can equate what the natural logs 
are taken of:

+%282x%2B1%29%28x-3%29+=+x%5E2+

+2x%5E2-6x%2Bx-3+=+x%5E2+

+2x%5E2-5x-3+=+x%5E2+

+x%5E2-5x-3+=+0+

x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+

x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%28-3%29+%29%29%2F%282%281%29%29+

x+=+%285+%2B-+sqrt%2825%2B12+%29%29%2F2+

x+=+%285+%2B-+sqrt%2837%29%29%2F2+ 

We discard the minus sign because it results in a 
negative value and the original equation contains
ln(x). Natural logarithms of negative numbers are
not real numbers. So the only solution is

x+=+%285+%2B+sqrt%2837+%29%29%2F2+

Edwin