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Logarithmic Rules

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Power rule for logarithms

$\log_b(m^p) = p\cdot\log_b(m)$

Zero exponent rule for logarithms

$\log_b(b^0) = 0$

Product rule for logarithms

$\log_b(mn) = \log_b(m) + \log_b(n)$

Quotient rule for logarithms

$\log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n)$

Logarithm of one

$\log_b(1) = 0$

Identity rule for logarithms

$b^{\log_b(m)} = m$

Change of base formula for logarithms

$\log_b(m) = \frac{\log_k(m)}{\log_k(b)}$

Logarithm of the base

$\log_b(b) = 1$

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