If log (x - 5) + log (x + 5) = 2 log 12, the positive value of x is :

1. 5

2. 13

3. 4.8

4. 12

Given,

⇒ log (x - 5) + log (x + 5) = 2 log 12

⇒ log (x - 5)(x + 5) = log 12²

⇒ log (x² + 5x - 5x - 25) = log 144

⇒ log (x² - 25) = log 144

⇒ x² - 25 = 144

⇒ x² = 144 + 25

⇒ x² = 169

⇒ x = $\sqrt{169}$

⇒ x = $\pm 13$.

So, positive value of x = 13.

Hence, Option 2 is the correct option.