February 2nd, 2011, 07:48 AM  #1 
Newbie Joined: Oct 2010 Posts: 6 Thanks: 0  Help solving a problem
Hi all, first post and I didn't know exactly where to put this. Does anybody know how to solve for x an equation of the form: 10 + ln(x) = 5x Thanks 
February 2nd, 2011, 10:25 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Help solving a problem
You have to use "numerical methods" to get approximate solutions.

February 2nd, 2011, 11:47 AM  #3 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Help solving a problem
If possible, rearrange so that the lefthand side is of the form and the righthand side is a constant, then take the Lambert W of both sides. The Lambert W is doublevalued over the interval [1/e, 0). This gives you two solutions, 0.00004541 and 2.15341058. 
February 2nd, 2011, 06:12 PM  #4 
Newbie Joined: Oct 2010 Posts: 6 Thanks: 0  Re: Help solving a problem
Thanks for the help! Never heard of the Lambert W before.

February 2nd, 2011, 06:14 PM  #5  
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Help solving a problem Quote:
 

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