Question

sa se verifice ca $lg \frac{1}{2} + lg \frac{2}{3} +.....+ lg \frac{9}{10} = -1$.

Answer 1

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