Logarithms

A logarithm is the inverse of an exponential function. So

\[\log_b x = y \iff b^y=x .\]

Log Rules

• $\log_b xy = \log_b x + \log_b y$
• $log_b \frac{x}{y} = \log_b x - \log_b y$
• $\log_b x^a = a \log_b x$
• $b^{\log_b x} = x$

Change of Base formula

$\log_a x = \frac{\log_b x}{\log_b a}$, for $a\neq 1$.