Solve the following equation for x:

log (x + 1) + log (x - 1) = log 11 + 2log 3

Given,

⇒ log (x + 1) + log (x - 1) = log 11 + 2log 3

⇒ log (x + 1)(x - 1) = log 11 + log 3²

⇒ log (x² - 1) = log (11 x 9)

⇒ log (x² - 1) = log 99

⇒ (x² - 1) = 99

⇒ x² = 99 + 1

⇒ x² = 100

⇒ x = 10, -10

In this case x ≠ -10 as (x + 1) and (x - 1) will be negative and log of only positive numbers are defined.

Hence, x = 10.