July 30th, 2010, 11:11 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, 03:00 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, 05:31 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, 06:35 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. 

Tags 
equation, solutions 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How many solutions to an equation  raycol1970  Algebra  3  April 14th, 2012 03:03 PM 
How many solutions are there to the equation?  Solarmew  Applied Math  12  November 21st, 2011 06:01 PM 
solutions of an equation  daivinhtran  Algebra  10  September 8th, 2011 03:20 PM 
Solutions to the equation  jakeward123  Calculus  5  June 3rd, 2011 01:17 AM 
How many solutions to an equation  raycol1970  Applied Math  1  December 31st, 1969 04:00 PM 