e^x is defined on [-, +]

e⁰ = 1

e¹ = e = 2.71828...

The inverse function to e^x is called ln x.

ln(e^x) = e^lnx = x

ln(x) is defined on ]0, +] and its graph is obtained by reflecting the graph y = e^x with respect to the line y = x.

ln(1) = 0

ln(e) = 1