engleski

On intersections of the exponential and logarithmic curves

We consider the curves y=a**x and y= loga(x) and their intersecting points for various bases a. Although this problem belongs to the elementary calculus, it turns out that the problem of determining number of these points, for a∈〈0, 1〉, is overlooked, so far. We prove that this number can be 0, 1, 2 or, even, 3, depending on the base a.

exponential function ; inflection ; stationary point ; homeomorphism

nije evidentirano