Ne folosim de urmatoarele reguli
[tex]\log_{c}{a}+\log_{c}{b}=\log_{c}{(a*b)}[/tex]
[tex]\log_{c}{a}-\log_{c}{b}=\log_{c}{\frac{a}{b}}[/tex]
[tex](a-b)(a+b)=a^{2}-b^{2}[/tex]
Atunci
[tex]\log_{2}{5-\sqrt{3}}+\log_{2}{5-\sqrt{3}}-\log_{2}{11}=\log_{2}{(5-\sqrt{3})(5+\sqrt{3})}-\log_{2}{11}=\log_{2}{(25-3)}-\log_{2}{11}=\log_{2}{\frac{22}{11}}=\log_{2}{2}=1[/tex]