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June 18th, 2015, 04:41 AM   #1
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Range of values of a

How do I find the range of values of a that satisfy this equation?

$\displaystyle \left |\frac{1-{ln}(a)+((1-{ln}(a))^{2}-4{ln}(a))^{1/2}}{2{ln}(a)} \right |+\left |\frac{1-{ln}(a)-((1-{ln}(a))^{2}-4{ln}(a))^{1/2}}{2{ln}(a)} \right |=\left |\frac{1-{ln}(a)}{{ln}(a)} \right |$
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June 18th, 2015, 05:15 AM   #2
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The first thing you should do is to simplify the left hand side.
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June 18th, 2015, 05:29 AM   #3
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Quote:
Originally Posted by v8archie View Post
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.
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June 18th, 2015, 12:50 PM   #4
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$\displaystyle 1-ln(a)\ge ((1-ln(a))^2-4ln(a))^{1/2}$ while ln(a) < 1 is a partial solution.
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June 18th, 2015, 10:32 PM   #5
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$\displaystyle 1-ln(a)\ge ((1-ln(a))^2-4ln(a))^{1/2}$ 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?
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June 19th, 2015, 12:35 PM   #6
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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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