Logarithm

Notations

Normal Log

\[\log_b (a)\]

Natural Log

If the base is e.

\[\log_e (a) = \ln (a)\]

Common Log

If the base is 10.

\[\log_{10} (a) = \lg (a)\]

Theorems

• \[\log_b 1 = 0\]
• \[\log_b b = 1\]
• \[\log_b ac = \log_b a + \log_b c\]
• \[\log_b \frac{a}{c} = \log_b a - \log_b c\]
• \[\log_b a^r = r \log_b a\]
• \[\log_b \frac{1}{c} = - \log_b c\]
• \[\log_b a = \frac{1}{\log_a b}\]