Question

Demonstrati ca:lg 1/2 lg 2/3 ... lg 9/10=-1

Answer 1

$lg(\frac{1}{\not2} * \frac{\not2}{\not3}*...*\frac{\not9}{10})= \\\\ =lg \ \frac{1}{10}= \\\\=lg \ 10^{-1} = \\\\ =\boxed{-1} \\\\\\\\ \boxed{\boxed{lg10=log_{10} \ 10}}$

Answer 2

$lg \frac{1}{2}+ lg \frac{2}{3}+lg \frac{3}{4}+lg \frac{4}{5}+ lg \frac{5}{6}+ lg \frac{6}{7}+ lg\frac{7}{8}+lg \frac{8}{9}+lg \frac{9}{10}$

lg1-lg2+lg2-lg3+lg3-lg4+lg4-lg5+lg5-lg6+lg6-lg7+lg7-lg8+lg8-lg9+lg9-lg10=


[tex]lg1-lg10= -1 lg1= log_{10}1=0 lg10=log_{10}10=1 [/tex]