# Math Help - Please solve logarithmic equation

1. ## Please solve logarithmic equation

Please help solve 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.

2. 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 $x=-1+\sqrt{1+e^4}$

3. Thank you