*Problem #7*

If 0 < *a* < 1, then the equation *a*^{x} = x
[*a^x = x*, if your viewer doesn't support superscripts] has a
unique solution, since the function on the left is strictly decreasing
while the function on the right is strictly increasing.
For which value of *a* > 1 does the equation *a*^{x} =
x have a unique solution?