Find all values of b such that the equation
b^{x} = log_{b}x
has exactly one real solution.
(In reply to
re(2): possible solutioncorrection 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 20121213 11:13:02 