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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    
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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
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