Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\log_8\,7}{\log_4\,7}$ is gelijk aan	A. 1,5
	B. 2
	C.
	D. log₄ 7
	E. log₂ 7

[ log_a b = ^alog b ]

[ 6-2604 - op net sinds 30.5.2020-(E)-17.11.2024 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\frac{\log_8\,7}{\log_4\,7}$ is equal to	A. 1.5
	B. 2
	C.
	D. log₄ 7
	E. log₂ 7

Oplossing - Solution

1^ste manier : overgang naar Briggse logaritmen
(met de 'Change Of Base Formula')
$\frac{\log_8\,7}{\log_4\,7}=\frac{\frac{\log7}{\log8}}{\frac{\log7}{\log4}}=\frac{\log4}{\log8}=\frac{\log2^2}{\log2^3}=\frac{2.\log2}{3.\log2}=\frac23$
2^de manier : overgang naar basis 2
$\frac{\log_8\,7}{\log_4\,7}=\frac{\frac{\log_27}{\log_28}}{\frac{\log_27}{\log_24}}=\frac{\log_24}{\log_28}=\frac23$