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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