Свойства логарифмов

#логарифмы

1. ${\log }_{a}bc={\log }_{a}b+{\log }_{a}c$
2. ${\log }_a\frac{b}{c}={\log }_{a}b-{\log }_{a}c$
3. ${\log }_a{b}^n=n{\log }_{a}b$
4. ${\log }_{a^k}b=\frac{1}{k}{\log }_{a}b$
5. ${\log }_{a^k}{b}^n=\frac{n}{k}{\log }_{a}b$
6. ${\log }_{a}b=\frac{{\log }_{d}b}{{\log }_{d}a}$
7. ${\log }_{a}b=\frac{1}{{\log }_{b}a}$
8. ${\log }_{a}b\cdot {\log }_{b}a=1$
9. $a^{lo{g}_{b}c}=c^{lo{g}_{b}a}$

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