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Logarithmic Rules

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Product rule for logarithms

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log⁡b(mn)=log⁡b(m)+log⁡b(n)\log_b(mn) = \log_b(m) + \log_b(n)

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Quotient rule for logarithms

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log⁡b(mn)=log⁡b(m)−log⁡b(n)\log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n)

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Power rule for logarithms

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log⁡b(mp)=p⋅log⁡b(m)\log_b(m^p) = p\cdot\log_b(m)

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Change of base formula for logarithms

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log⁡b(m)=log⁡k(m)log⁡k(b)\log_b(m) = \frac{\log_k(m)}{\log_k(b)}

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Logarithm of one

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log⁡b(1)=0\log_b(1) = 0

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Logarithm of the base

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log⁡b(b)=1\log_b(b) = 1

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Identity rule for logarithms

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blog⁡b(m)=mb^{\log_b(m)} = m

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Zero exponent rule for logarithms

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log⁡b(b0)=0\log_b(b^0) = 0

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