Re: mathematics and reasoning questions

Posted by Amit Goyal on Oct 05, 2011; 2:15am
URL: http://discussion-forum.276.s1.nabble.com/mathematics-and-reasoning-questions-tp6831618p6860761.html

for 0 < x < 1, log x < 0 < x
for x = 1, log x = 0 < 1
for x > 1, f(x) = x  - log x is an increasing function (because f'(x) = 1 - 1/x > 0) and we know that f(x) is continuous everywhere on (0, ∞). Thus, f(1) > 0  and f'(x) > 0 implies that f(x) > 0 for x > 1.