# Please solve logarithmic equation

• Nov 15th 2007, 06:15 AM
oceanmd
Please solve logarithmic equation
ln x + ln (x + 2) = 4
ln x (x + 2) = 4
e ^ 4 = x (x + 2)

What do I do next to solve for x?

Thank you.
• Nov 15th 2007, 06:20 AM
red_dog
First of all we have to put the conditions for the existence of the logarithms:
$x>0, \ x+2>0\Rightarrow x\in(0,\infty)$.
Now solve the quadratic $x^2+2x-e^4=0$ and choose the right solution which is $x=-1+\sqrt{1+e^4}$
• Nov 15th 2007, 06:59 AM
oceanmd
Thank you