oblicz wartość wyrażenia; [latex]log_{2}48 - log_{2}3\ log _{3}frac{1}{6}+log_{3}frac{2}{3}\ 2log_{frac{1}{2}}sqrt{3}+log_{frac{1}{2}}5frac{1}{3}\ (log_{5}16-log_{5}80)^{2} \ log_{frac{2}{3}4-2log_{frac{2}{3}3[/latex]

[latex] log_{2}48 - log_{2}3=log_{2}frac{48}{3}=log_{2}16=4[/latex] [latex]log _{3}frac{1}{6}+log_{3}frac{2}{3}=log_{3}(frac{1}{6}*frac{2}{3})=log_{3}frac{1}{9}=-2[/latex] [latex]2log_{frac{1}{2}}sqrt{3}+log_{frac{1}{2}}5frac{1}{3}=log_{frac{1}{2}}(sqrt3)^2+log_{frac{1}{2}}frac{16}{3}=log_{frac{1}{2}}3+log_{frac{1}{2}}frac{16}{3}=\ log_{frac{1}{2}}(3*frac{16}{3})=log_{frac{1}{2}}16=-4[/latex] [latex] (log_{5}16-log_{5}80)^{2} =(log_5frac{16}{80})^2=(log_5frac{1}{5})^2=(-1)^2=1[/latex] [latex] log_frac{2}{3}4-2log_frac{2}{3}3=log_{frac{2}{3}}4-log_{frac{2}{3}}9= log_{frac{2}{3}}frac{4}{9}=2[/latex]    liczę na naj