let-x-and-y-be-two-real-numbers-if-x-y-10-prove-ln-x-1-ln-y-1-2ln6-

Question Number 56477 by problem solverd last updated on 17/Mar/19

let x and y be two real numbers

if x + y ⩽ 10 prove

\ln (x + 1) + \ln (y + 1) ⩽ 2 \ln 6

Answered by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19

x + y ⩽ 10

(x + 1) + (y + 1) ⩽ 12

\frac{(x + 1) + (y + 1)}{2} ⩾ \sqrt{(x + 1) ((y + 1)}

6 ⩾ \sqrt{(x + 1) (y + 1)}

36 ⩾ (x + 1) (y + 1)

l n (36) ⩾ l n (x + 1) + l n (y + 1)

2 l n 6 ⩾ l n (x + 1) + l n (y + 1)