Solve for x :

log (x + 2) + log (x − 2) = log 5

Given,

⇒ log (x + 2) + log (x − 2) = log 5

⇒ log [(x + 2) × (x − 2)] = log 5

⇒ log [(x² - 2²)] = log 5

⇒ log [(x² - 4)] = log 5

⇒ (x² - 4) = 5

⇒ x² = 5 + 4

⇒ x² = 9

⇒ x = $\sqrt{9}$

⇒ x = ± 3.     

x cannot be equal to -3 as that will make x + 2 = -3 + 2 = -1, that is negative, and argument of a logarithm cannot be negative.

Hence, the value of x = 3.