Introduction 1: A function of the form $y(x)=a^x$, where $a$ ($a \neq 1)$ is a positive number, is called an exponential function with base $a$.
Introduction 2: A function of the form $y(x)=\;^a\!\log x, (x>0)$, where $a$ ($a\neq 1$) is a positive number is called a logarithmic function with base $a$.
Theorem:
Introduction 2: A function of the form $y(x)=\;^a\!\log x, (x>0)$, where $a$ ($a\neq 1$) is a positive number is called a logarithmic function with base $a$.
Theorem:
- $y = ^a\!\log a^y$
- $x = a^{^a\!\log x}$