Question

Solve the following:
log ( x + 1) + log ( x - 1) = log 11 + 2 log 3

Answer 1

log ( x + 1) + log ( x - 1) = log 11 + 2 log 3
⇒ log [(x + 1)(x - 1)] = log 11 + log 3²
⇒ log {x² - 1} = log (11.9)
⇒ log {x² - 1} = log99
⇒ x² - 1 = 99
⇒ x² = 100
So, x = 10 or -10
Negative value is rejected
So, x = 10.