Question 212873
Well to do this problem we need to use 2 properties of ln.  <br>

1.  {{{ln(xy) = ln(x) + ln(y)}}}
2.  {{{e^(ln(x)) = x}}}<br>

Now that we have those out of the way we can solve the equation.  First we need to use property 1 on the equation.  We get:<br>

{{{ln (x - 5) + ln (x + 4) = ln 36}}}
{{{ln((x-5)(x+4)) = ln 36}}}<br>

Now we use propterty 2 by raising both sides to the e power.  <br>

{{{ln((x-5)(x+4)) = ln 36}}}
{{{e^(ln((x-5)(x+4))) = e^(ln 36)}}}
{{{(x-5)(x+4) = 36}}}<br>

And now we solve the quadratic equation.<br>

(x-5)(x+4) = 36
x^2-x-20 = 36
x^2-x-56 = 0
(x-8)(x+7)=0<br>

so x = -7 and x = 8.  If you check those solutions you will find that indeed they work.