Cat este 4 la puterea log in baza 2 din 3?

Salut,

Notăm cu x treaba din enunț.

[tex]x=4^{log_23}.\ Logaritm\breve{a}m\ \^{i}n\ baza\ 2:[/tex]

[tex]\log_2x=log_2(4^{log_23})\Rightarrow\log_2x=log_23\cdot log_24,\ sau\ log_2x=log_23\cdot log_22^2\Rightarrow[/tex]

[tex]\Rightarrow log_2x=log_23 \cdot 2\cdot log_22,\ sau\ log_2x=2\cdot log_23\Rightarrow log_2x=log_23^2,[/tex]

deci x = 3² = 9.

Green eyes.

4=2²

(2²)^log₂3=(2)²*log₂3=2^log₂3²=2^log₂9=9