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 
Newbie Joined: Oct 2014 From: Australia Posts: 27 Thanks: 10  
June 18th, 2015, 12:50 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733 
$\displaystyle 1ln(a)\ge ((1ln(a))^24ln(a))^{1/2}$ while ln(a) < 1 is a partial solution.

June 18th, 2015, 10:32 PM  #5 
Newbie Joined: Oct 2014 From: Australia Posts: 27 Thanks: 10  
June 19th, 2015, 12:35 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  

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absolutes, range, values 
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