Question

sa se rezolve in multimea numerelor reale ecuatia log in baza 2 din x + log in baza 4 din x + log in baza 8 din x = 11/6

Answer 1

In general stim ca
$\log_{a^{n}}{b}=\frac{1}{n}\log_{a}{b}$
Atunci ecuatia devine
$\log_{2}{x}+\log_{2^{2}}{x}+\log_{2^{3}}{x}=\log_{2}{x}+\frac{1}{2}\log_{2}{x}+\frac{1}{3}\log_{2}{x}=\frac{6+3+2}{6}\log_{2}{x}=\frac{11}{6}\log_{2}{x}=\frac{11}{6}\Rightarrow \log_{2}{x}=1\Rightarrow x=2$

Answer 2

Raspunsul il ai in poza