te folosesti de relatia
[tex]\lg{a}+\lg{b}=\lg{a*b}[/tex]
Atunci
[tex]lg{\frac{1}{2}}+lg{\frac{2}{3}}+...+\lg{\frac{8}{9}}+lg{\frac{9}{10}}=lg{\frac{1}{2}*\frac{2}{3}*\frac{3}{4}*..*\frac{8}{9}*\frac{9}{10}}=lg{\frac{1}{10}}=\lg{10^{-1}}=\log_{10}{10^{-1}}=-1[/tex]
