Question

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

Answer 1

We may use,

1. log (a) + log (b) = log (ab)

2. a · log (b) = log (b^a)

So,

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

=> log [(x + 1)(x - 1)] = log (2³) + log (3)

=> log (x² - 1) = log (8) + log (3)

=> log (x² - 1) = log (8 · 3)

=> log (x² - 1) = log (24)

So, we get,

x² - 1 = 24

=> x² - 1 - 24 = 0

=> x² - 25 = 0

=> (x - 5)(x + 5) = 0

=> x = 5 ; x = - 5

Hence the answer is ± 5.