Question

logaritm baza 2 din 2/3 = log baza 2 din 2 la puterea-3?
Am gasit informatia intr-un caiet mai vechi , si imi pare eronata...
va multumesc pentru suport.

Answer 1

   
[tex]\displaystyle\\ \text{Presupunem ca afirmatia este adevarata.}\\\\ \log_2 \Big(\frac{2}{3}\Big) = \log_2 \Big(2^{-3}\Big)\\\\ \Longrightarrow~~~ \frac{2}{3} = 2^{-3} ~~ \Longleftrightarrow~~ \frac{2}{3} =\frac{1}{2^3}~~ \Longleftrightarrow~~ \frac{2}{3} =\frac{1}{8}~~~\boxed{\textbf{FALS}}\\\\ \Longrightarrow~~~\boxed{\log_2 \Big(\frac{2}{3}\Big) \neq \log_2 \Big(2^{-3}\Big)} [/tex]