Solve for x :

log (x + 5) + log (x - 5) = 4 log 2 + 2 log 3

Given,

⇒ log (x + 5) + log (x - 5) = 4 log 2 + 2 log 3

⇒ log (x + 5)(x - 5) = log 2⁴ + log 3²

⇒ log (x² - 5x + 5x - 25) = log (2⁴ × 3²)

⇒ log (x² - 25) = log (16 × 9)

⇒ log (x² - 25) = log 144

⇒ x² - 25 = 144

⇒ x² = 144 + 25

⇒ x² = 169

⇒ x = $\sqrt{169} = \pm 13$.

Since, x cannot be negative as that will make (x + 5) and (x - 5) negative.

Hence, x = 13.