# How do you solve lnx-ln(x+2)=1?

$x = \frac{2 e}{1 - e}$

#### Explanation:

$\ln x - \ln \left(x + 2\right) = 1$

$\ln \left(\frac{x}{x + 2}\right) = \ln e \text{ " }$because $\ln e = 1$

$\frac{x}{x + 2} = e$

$x = e \left(x + 2\right)$

$x = e x + 2 e$

$x - e x = 2 e$

$x \left(1 - e\right) = 2 e$

$\frac{x \left(1 - e\right)}{\left(1 - e\right)} = \frac{2 e}{1 - e}$

$\frac{x \cancel{\left(1 - e\right)}}{\cancel{\left(1 - e\right)}} = \frac{2 e}{1 - e}$

$x = \frac{2 e}{1 - e}$

God bless...I hope the explanation is useful.