Originally Posted by
DanielJackson if
(1/b) < [(ln b - ln a)/(b-a)] < (1/a)
then
(1/b) < (1/a) -- by simply ignoring the middle expression of the inequality
thus,
b > a
What if b<0 and a>0 ? Then it would be come a>b
* now we must show that 'a' is greater than 0.
if
b > a
then
ln b > ln a
If a<0 then ln a is not defined, so here you have assumed that 0<a<b which is
the thing you are trying to prove.
thus,
[(ln b - ln a)/(b-a)] > 0
if
0 < [(ln b - ln a)/(b-a)] < (1/a)
then
(1/a) > 0
thus,
a > 0
and therefore,
0 < a < b