# How do you solve 3000/(2+e^(2x))=2?

The answer is $x = \frac{1}{2} \ln \left(1498\right) = \ln \left(\sqrt{1498}\right) \approx 3.65594$
First, multiply both sides by $2 + {e}^{2 x}$ and divide both sides by 2 to get $2 + {e}^{2 x} = 1500.$ Subtracting 2 from both sides leads to ${e}^{2 x} = 1498$. Now take the natural logarithm of both sides and then divide both sides by 2 to get the final answer:
$x = \frac{1}{2} \ln \left(1498\right) = \ln \left(\sqrt{1498}\right) \approx 3.65594$.