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Table of Contents
Logarithms and Exponentials
An exponential is $a^x=n$, a logarithm is $\log_{a}n=x$ where $a$ is the base, $x$ is the power, and $n$ is the result. Exponentials and logarithms are inverses of eachother. The constant $e$ is a special case, in which its inverse is the natural log, or $\ln n=x$, which is equivalent to $log_{e}n=x$.
Useful Properties
One-to-One Property
This property applies to equations that look like $a^x = a^y$. If $x = y$, then you can drop the exponent. The same works for logs (i.e. $\ln x = \ln y$ → $x = y$).
Inverse Property
- $a^{\log_{a}x} = x$
- $\log_{a}a^x = x$
