Wiskunde Multiple Choice Vraag

Wat is het verbandtussen a = log₆ 108 en b = log₂ 3.	A. $b=\frac{a+2}{3+a}$
	B. $b=\frac{a-2}{3+a}$
	C. $b=\frac{2-a}{3+a}$
	D. $b=\frac{a-2}{3-a}$
	E. $b=\frac{3+a}{a+2}$

[ 6-8874 - op net sinds 2.5.2024-(E)- ]

Translation in E N G L I S H

IN CONS IN CONSTR IN CONSTRUC IN CONSTRUCTI IN CONSTRUCTION	A.
	B.
	C.
	D.
	E.

Oplossing - Solution

$\\a=\log_6108=\frac{\log_2\:(36.3)}{\log_26}=\frac{\log_26^2+\log_23}{\log_26}=2+\frac{\log_23}{\log_22+\log_23}\\=2+\frac{b}{1+b}=\frac{2+2b+b}{1+b}=\frac{2+3b}{1+b}$ Hieruit volgt dat a(1 + b) = (2 + 3b)
⇔ a + ab = 2 + 3b ⇔ (a − 3)b = 2 − a ⇔ b = (2 − a)/(a − 3) = (a − 2)/(3 − a)