Question

Calculati: log in baza 1\8 din 8.

Answer 1

login baza 2^(-3) din 2³= (3/(-3)) *log in baza 2 din 2= (-1) *1=-1

 ALTFEL
la ce putere trebuie ridicat 1/8=2^(-3) ca sa dea 8=2^3???
 (2^(-3)) ^x=2³
2^(-3x)=2³
-3x=3
x=3/(-3)
x=-1

Answer 2

$\log_{\dfrac{1}{8}} 8 =\dfrac{1}{\log_\Big8 \dfrac{1}{8}} = \\ \\ = \dfrac{1}{\log_\Big8 8^{-1}} = \dfrac{1}{-\log_\Big8 8} \\ \\ = - \dfrac{1}{\log_\Big8 8} =-\dfrac{1}{1} = \\ \\ =-1$