Logarithms

Logarithm of one

$log_{a}(1) = 0$

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Logarithm of base

$log_{a}(a) = 1$

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Sum of logarithms

$log_{a}(x\cdot y) = log_{a}(x)+log_{a}(y)$

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Difference of logarithms

$log_{a}(\frac{x}{y}) = log_{a}(x)-log_{a}(y)$

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Logarithm of power

$log_{a}(x^{n}) = n\cdot log_{a}(x)$

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Logarithm and the power of base

$log_{a^n}(x) = \frac{1}{n}\cdot log_{a}(x)$

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Logarithm and the power of base

$log_{a}(x)\cdot log_{x}(a) = 1$

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Changing the logarithm base

$log_{a}(x) = \frac{log_{b}(x)}{log_{b}(a)}$

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