Question 1001179
<pre>
{{{ ln(2x+1) + ln(x-3) - 2 ln(x) = 0 }}}

{{{ ln((2x+1)(x-3)^"") - ln(x^2) = 0 }}}

{{{ ln((2x+1)(x-3)^"") = ln(x^2) }}}

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

{{{ (2x+1)(x-3) = x^2 }}}

{{{ 2x^2-6x+x-3 = x^2 }}}

{{{ 2x^2-5x-3 = x^2 }}}

{{{ x^2-5x-3 = 0 }}}

{{{x = (-b +- sqrt( b^2-4ac ))/(2a) }}}

{{{x = (-(-5) +- sqrt( (-5)^2-4(1)(-3) ))/(2(1)) }}}

{{{x = (5 +- sqrt(25+12 ))/2 }}}

{{{x = (5 +- sqrt(37))/2 }}} 

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 = (5 + sqrt(37 ))/2 }}}

Edwin</pre>