Wiskunde Multiple Choice Vraag

Bereken log₄ 39,2 in functie van a = log₇ 2 en b = log₂ 10	A. $\frac1a+\frac23-\frac b2$
	B. $\frac1a+\frac32-\frac b2$
	C. $\frac1a-\frac32+\frac b2$
	D. $\frac1a-\frac23+\frac b2$
	E. $\frac1a-\frac23+\frac b3$

[ 6-8873 - 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

$\\\log_4 39,2=\log_4\frac{392}{10}=\log_4\frac{49.8}{10}=\log_47^2+\log_42^3-\log_410\\=2\log_47+3\log_42-\frac{\log_210}{\log_24}=2.\frac{\log_27}{\log_24}+\frac{3}{\log_24}-\frac{\log_210}{2}\\=\frac{1}{\log_72}+\frac{3}{\log_24}-\frac{b}{2}=\frac 1a+\frac 32-\frac b2$