If x = log 5 3 + log 7 5 + log 9 7 , then

Step-by-step solution

We have, x = log 5 3 + log 7 5 + log 9 7 Using AM ≥ GM for three positive real numbers a + b + c 3 ≥ a b c 1 3 . Equality holds when a = b = c . ∴   log 5 3 + log 7 5 + log 9 7 3 > log 5 3 · log 7 5 · log 9 7 1 / 3 ⇒   x > 3 log 3 log 5 × log 5 log 7 × log 7 log 9 1 / 3 ⇒   x > 3 1 2 1 / 3 ⇒ x > 3 2 3