[latex]c) x=4log10-log100=log10^{4}-log10^{2}=logfrac{10^{4}}{10^{2}}=log10^{2}=\=2log10=2\ d)x=frac{3}{4}log1-2log1000 00=frac{3}{4}cdot0-2log10^{6}=-2cdot6log10=-12 \[/latex] [latex]e) x= 2log10^{-3}+logsqrt[3]{10}=log(10^{-3})^2+log10^{frac{1}{3}}=\=log(10^{-6}cdot10^{frac{1}{3}})=log10^{-frac{17}{3}}=-frac{17}{3} log10=-5frac{2}{3} \ f) x = -frac{1}{2}log10000-frac{1}{6}log10^{-4}=log(10^{4})^{-frac{1}{2}}-log(10^{-4})^{frac{1}{6}}=\=log({10^{-2}}:{10^{-frac{4}{6}})=log10^{-2+frac{2}{3}}=-1frac{1}{3}log10=-1frac{1}{3}[/latex] albo zupełnie prosto: [latex]c) x=4log10-log100=4-log10^{2}=4-2log10=4-2=2\ d)x=frac{3}{4}log1-2log1000 00=frac{3}{4}cdot0-2log10^{6}=-2cdot6log10=-12 \e) x= 2log10^{-3}+logsqrt[3]{10}=2cdot (-3)log10+log10^{frac{1}{3}}=\=-6+frac{1}{3}log10=-6+frac{1}{3}=-5frac{2}{3}\ f) x = -frac{1}{2}log10000-frac{1}{6}log10^{-4}=-frac{1}{2}log10^{4}-frac{1}{6}cdot(-4)log10=\=-frac{1}{2}cdot4log10+frac{4}{6}=-2+frac{2}{3}=-1frac{1}{3}[/latex]
