Question

sa se calculeze log in baza 2 din 2 supra 3 +log in baza 2 din 3 supra 4 +...+log in baza 2 din 7 supra 8

Answer 1

[tex]\text{Folosim formula:}\ \log_{a}b+\log_{a} c=\log _{a} {b\cdot c}\\ \text{Deci vom avea:}\\ \log_{2}\dfrac{2}{3}+\log_{2}\dfrac{3}{4}+\dots+\log_{2} \dfrac{7}{8}=\log_{2} \left(\dfrac{2}{3}\cdot \dfrac{3}{4}\cdot _{\dots} \cdot \dfrac{7}{8}\right)=\log_{2} \dfrac{2}{8}=\boxed{-2}[/tex]