1. The problem statement, all variables and given/known data verify that f(x) = log(1+ex) is convex and use this to show that (1+x1)1/n(1+x2)1/n..(1+xn)1/n >= 1 + (x1x2...xn)1/n where x1,x2,...xn are positive real numbers. 2. Relevant equations 3. The attempt at a solution I know f(x) is convex b/c f''(x) is always positive. and I can guess the above ineqality is true, but I do not konw how I use the f(x) to prove the inequality. Can log (1+e^x) imply to (1+x1)1/n...(1+xn)1/n..?