1. it would be much easier if he draw 3^x and 4-x and find values where 4-x is "bigger" then 3^x
2. I do not what made you think that if they're "monotically increasing there exists only one solution"?
example: x^3+5 and 3^x, both monotonically increasing but have 2 intersections.
There is no algebraic solution, but there is a graphical solution.Solve: .
We have: .
The question becomes: when is below ?
The graphs look like this:Code:| * | * * | * * | o | * : * * : * * | : * * | : * - - - - - - + - + - - - - * - - | 1 * |
As you pointed out, the curves intersect at
You answer is correct: .