Exponentials and logarithms

Graphs of eˣ, ln x and related functions, with a movable probe, a parameter a, and a box for your own expression.

Figure 1.1.Choose a scenario, then drag the probe and the parameter a. The list shows each curve’s value at the probe. Type an expression in a to add a curve. Open on its own

eˣ and ln x are inverse functions, so their graphs are reflections in the line y = x. This is why ln x is defined only for x > 0.

Substituting u = eˣ turns an exponential equation into a polynomial in u. A root with u ≤ 0 gives no solution for x.