[tex]\displaystyle\\
\text{Folosim formula: } ~~~\boxed{\log_ab + \log_ac = \log_a (b\times c)}\\\\
\log_2\frac{2}{1}+\log_2\frac{3}{2}+\log_2\frac{4}{3}+\log_2\frac{5}{4}+\log_2\frac{6}{5}+\log_2\frac{7}{6}+\log_2\frac{8}{7}=\\\\
=\log_2\left(\frac{2}{1}\times\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\right) =\log_2\frac{8}{1}=\log_2 8 = \boxed{\bf 3}\\\\
_\text{Se simplifica numaratorul fractiei din stanga cu numitorul fractiei din dreapta.}\\
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