Question

lg1/2+lg2/3+.... +lg9/10=-1​

Answer 1

Răspuns:

lg1/2=lg1-lg2

lg2/3=lg2-lg3

...........................

lg9/10=lg9-lg10

-----------------------se  aduna   membru  cu  membru

lg1/2+lg2/3+...+lg9/10=lg1-lg2+lg2-lg3+....+lg9-lg10=0-0+....+0-1=

=-1

Explicație pas cu pas:

Answer 2

$\displaystyle \lg\frac{1}{2}+\lg\frac{2}{3}+\lg\frac{3}{4}...+\lg\frac{9}{10}= \\ \\ =\lg\Big(\frac{1}{2}\cdot \frac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot \frac{8}{9}\cdot \frac{9}{10}\Big) = \\ \\ = \lg\Big(\dfrac{1}{10}\Big) = \lg 10^{-1} =-\lg 10 = -1$