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Are these all the laws of logarithms?

1. $\log_{a}(1)=0$
2. $\log_{a}(a)=1$
3. $\log_{a}(x\,.\, y) = \log_{a}(x) + \log_{a}(y)$
4. $\log_{a}\left(\frac{x}{y}\right) = \log_{a}(x) - \log_{a}(y)$
5. $\log_{a}(x^b) = b \log_{a}(x)$
6. $\log_{a}\left(\sqrt[b]{x}\right) = \frac{\log_{a}(x)}{b}$

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