July 30th, 2010, 10:11 PM  #1 
Newbie Joined: Nov 2009 Posts: 15 Thanks: 0  Solutions to an equation
Hi, How can i prove that the equation (lnx)^3 = x has three real solutions? By using the Intermediate value theorem, i know that this equation has some solutions. I'm also trying to use Rolle's theorem but it's not getting me anywhere. Thanks for any help 
July 31st, 2010, 02:00 AM  #2 
Senior Member Joined: Apr 2010 Posts: 105 Thanks: 0  Re: Solutions to an equation
Are you sure? lnx is symmetric, so is the cube of it. There are two real solutions, between 1 and 0, 6 and 7. 
July 31st, 2010, 04:31 AM  #3 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Solutions to an equation
a third one as well, between 93 and 94. Hoempa 
July 31st, 2010, 05:35 AM  #4 
Senior Member Joined: Apr 2010 Posts: 105 Thanks: 0  Re: Solutions to an equation
Yes, there is a third one. f(x)=ln³x, use f'(x) with x>0. 

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