How do you solve ln x + ln (x+3) = 1?

Sep 25, 2016

$x \cong 0.72896$

Explanation:

$\ln x + \ln \left(x + 3\right) = 1$

$\ln \left(x \cdot \left(x + 3\right)\right) = 1$

$x \left(x + 3\right) = {e}^{1} = e$

${x}^{2} + 3 x - e = 0$

$x = \frac{- 3 \pm \sqrt{9 + 4 e}}{2}$

$\cong \frac{- 3 \pm \sqrt{9 + 10.87313}}{2}$

$\cong \frac{- 3 \pm 4.45793}{2}$

Since $\ln x$ is defined for $x > 0$

$x \cong \frac{- 3 + 4.45793}{2}$

$x \cong 0.72896$