Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

\(\large\boldsymbol{2^{log_4 12}}\) is gelijk aan (\(\scriptsize log_4 3 = {}^4\log 3\))	A. \(2\sqrt3\)
B. \(2^\sqrt3\)
C. \(\sqrt3\)
D. \(2^{log_43}\)
E. \(8\)

$\large\boldsymbol{2^{log_4 12}}$ equals	A. $2\sqrt3$
	B. $2^\sqrt3$
	C. $\sqrt3$
	D. $2^{log_43}$
	E. $8$

1^ste manier :
$\\2^{\log_412}=2^{\frac{\log_212}{\log_24}}=2^{\frac{\log_2(4.3)}{2}}=2^{\frac{\log_24+\log_23}{2}}=2^{\frac{2+\log_23}{2}}=2^{1+\frac{\log_23}{2}}\\=2.2^{\frac{\log_23}{2}}=2.2^{\frac12\log_23}=2.2^{\log_23^{\frac12}}=2.2^{\log_2\sqrt3}=2\sqrt3$
2^de manier :
$2^{\log_412}=\left(4^{\frac12}\right)^{\log_412}=4^{\frac12\log_4{12}}=4^{\log_412}=\sqrt{12}=\sqrt{4.3}=2\sqrt3$

\(\large\boldsymbol{2^{log_4 12}}\) equals	A. \(2\sqrt3\)
	B. \(2^\sqrt3\)
	C. \(\sqrt3\)
	D. \(2^{log_43}\)
	E. \(8\)