All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Exp=log (Posted on 2012-12-12) Difficulty: 2 of 5
Find all values of b such that the equation

bx = logbx

has exactly one real solution.

See The Solution Submitted by Jer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 8 of 9 |
(In reply to Solution by Harry)

As broll has noted, when b < e^(-e) ~= 0.06598803585 there are two solutions. As an example, when b~= 0.05 there's a second solution where x ~= .1373594001 and y ~= 0.6626608316, in addition to the solution where x=y (x ~= 0.35022485364, y = x).

Both curves are decreasing and concave up, one (the log curve) having more concavity than the other allowing for the two solutions.

  Posted by Charlie on 2012-12-13 16:18:18
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information