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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(3): possible solution--correction | Comment 6 of 9 |
(In reply to re(2): possible solution--correction by broll)

You are missing a solution. There is a solution with b>1.

When I thought this problem up I only thought of this solution.  I thought it was easy enough to find that I called it D2.

After submitting I realized b<1 would also give solutions.  I thought this was interesting but didn't change anything, assuming 0<b.

Your solution was a pleasant surprise.  In retrospect this problem is a bit tougher than D2.  You aren't done yet.

  Posted by Jer on 2012-12-13 11:13:02

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