Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{4^{log_3\, 18}}{2^{log_3\, 4}}$ is gelijk aan	A. 4
	B. 8
	C. 9
	D. 16
	E. 24

[ 6-8554 - op net sinds 24.10.2020-(E)-4.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\frac{4^{log_3\, 18}}{2^{log_3\, 4}}$ is equal to	A. 4
	B. 8
	C. 9
	D. 16
	E. 24

Oplossing - Solution

1^ste manier :
$\frac{4^{\log_3\,18}}{2^{\log_3\,4}}=\frac{2^{2(\log_3 9+\log_3 2)}}{2^{\log_3 2^2}}=\frac{2^{4+2.\log_3 2}}{2^{2.\log_3 2}}=2^4=16$
2^de manier :
$\frac{4^{\log_3\,18}}{2^{\log_3\,4}}=\frac{4^{\log_3\,(9.2)}}{2^{\,2.\log_3\,2}}=\frac{4^{\log_3 9+\log_3 2}}{4^{\log_3 2}}=4^{\log_3 9}=4^2=16$