log a x y 2 = log a x y − log a 2 {\displaystyle \log _{a}{xy \over 2}=\log _{a}{xy}-\log _{a}{2}}
log a x 3 y 5 = log a x 3 + log a y 5 {\displaystyle \log _{a}{x^{3}}{y^{5}}=\log _{a}{x^{3}}+\log _{a}{y^{5}}}
log a ( √ x y z ) = log a x 1 2 − log a y − log a z {\displaystyle \log _{a}\left({\frac {\surd {x}}{yz}}\right)=\log _{a}{x^{1 \over 2}}-\log _{a}{y}-\log _{a}{z}}
log a ( x 2 √ y z 3 ) = log a x 2 + log a y 1 2 − log a z 3 {\displaystyle \log _{a}\left({\frac {x^{2}{\surd {y}}}{\sqrt[{3}]{z}}}\right)=\log _{a}{x^{2}}+\log _{a}{y^{1 \over 2}}-\log _{a}{\sqrt[{3}]{z}}}
![{\displaystyle \log _{a}\left({\frac {x^{2}{\surd {y}}}{\sqrt[{3}]{z}}}\right)=\log _{a}{x^{2}}+\log _{a}{y^{1 \over 2}}-\log _{a}{\sqrt[{3}]{z}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28dfda88a040ed8c89bf2d3ed9e44559de9cd367)
