How do you solve ln (x + 2) + ln (x - 2) = 0?

Jun 23, 2016

$x = \sqrt{5}$

Explanation:

$\ln \left(x + 2\right) + \ln \left(x - 2\right) = 0$ is equivalent to

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

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

or ${x}^{2} - 4 = 1$

or ${x}^{2} - 5 = 0$

or $\left(x + \sqrt{5}\right) \left(x - \sqrt{5}\right) = 0$

or $x = - \sqrt{5}$ or $x = \sqrt{5}$

But as $x = - \sqrt{5}$ is not in domain (as log of negative number is not possible) hence $x = \sqrt{5}$