Jeżeli a>0, b>0, c>0 oraz a≠1 i b≠1, to: ${\log }_{b}c=\frac{{\log }_{a}c}{{\log }_{a}b}$   Zachodzi także własność: ${\log }_{b}a=\frac{1}{{\log }_{a}b}$

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$\text{a)}\frac{{\log }_{4}8}{{\log }_{4}6}={\log }_{6}8$  

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$\text{b)}\frac{{\log }_{100}2}{{\log }_{100}\frac{1}{3}}={\log }_{\frac{1}{3}}2$  

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$\text{c)}\frac{{\log }_{20}0,1}{{\log }_{20}3,5}={\log }_{3,5}0,1$  

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$\text{d)}\frac{{\log }_{\frac{1}{3}}\frac{1}{2}}{{\log }_{\frac{1}{3}}\frac{1}{5}}={\log }_{\frac{1}{5}}\frac{1}{2}$  

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$\text{e)}\frac{{\log }_{\sqrt{6}}7}{{\log }_{\sqrt{6}}12}={\log }_{12}7$  

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$\text{f)}\frac{{\log }_9\sqrt{10}}{{\log }_9\sqrt{5}}={\log }_{\sqrt{5}}\sqrt{10}$