My Math Forum Range of values of a

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 June 18th, 2015, 04:41 AM #1 Newbie     Joined: Oct 2014 From: Australia Posts: 27 Thanks: 10 Range of values of a How do I find the range of values of a that satisfy this equation? $\displaystyle \left |\frac{1-{ln}(a)+((1-{ln}(a))^{2}-4{ln}(a))^{1/2}}{2{ln}(a)} \right |+\left |\frac{1-{ln}(a)-((1-{ln}(a))^{2}-4{ln}(a))^{1/2}}{2{ln}(a)} \right |=\left |\frac{1-{ln}(a)}{{ln}(a)} \right |$
 June 18th, 2015, 05:15 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,691 Thanks: 2670 Math Focus: Mainly analysis and algebra The first thing you should do is to simplify the left hand side.
June 18th, 2015, 05:29 AM   #3
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 Originally Posted by v8archie The first thing you should do is to simplify the left hand side.
How? Other than cancelling the ln(a) on the bottom of all of them.

 June 18th, 2015, 12:50 PM #4 Global Moderator   Joined: May 2007 Posts: 6,835 Thanks: 733 $\displaystyle 1-ln(a)\ge ((1-ln(a))^2-4ln(a))^{1/2}$ while ln(a) < 1 is a partial solution.
June 18th, 2015, 10:32 PM   #5
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 Originally Posted by mathman $\displaystyle 1-ln(a)\ge ((1-ln(a))^2-4ln(a))^{1/2}$ while ln(a) < 1 is a partial solution.
This is useful, but I would like to know how you arrived at this. Was it by assuming that the solutions must be real?

June 19th, 2015, 12:35 PM   #6
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 Originally Posted by base12masterrace This is useful, but I would like to know how you arrived at this. Was it by assuming that the solutions must be real?
I assumed a real and positive.

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