Kissing Curves
Author: Steve Arnold
Date: 18/06/06

At exactly what value of x do the curves y = a^x and y = loga(x) kiss?

Use the slider to try different values for the base "a".

Now try and prove your result algebraically!

Drag Me!

At exactly what values of a and x
do the curves a^x and loga(x) kiss?

a = 3 (slider from 0 to 5, step 0.0010)
f(x) = log(x) / log(a)
g(x) = a^(x)
A = (10.433333333333334, 5.2)
K = (0, 0)