If [math]a[/math] is any positive real number other than 1, the base [math]a[/math] exponential function [math]f\left(x\right)=a^x[/math] is one-to-one. It therefore has an inverse. Its inverse is called the [i]logarithm function with base[/i] [math]a[/math].[br][br][b]Definition[/b]. The logarithm function with base [math]a[/math], [math]y=log_ax[/math], is the inverse of the base [math]a[/math] exponential function [math]y=a^x[/math] [math]\left(a>0,a\ne1\right)[/math].