Wiskunde Multiple Choice Vraag

log₅ 16 . log₈ 125 is gelijk aan	A. 5
B. 10
C. 15
D. 4
E. 1,25
F. 36

log₅ 16 . log₈ 125 is equal to	A. 5
	B. 10
	C. 15
	D. 4
	E. 1.25
	F. 36

1^ste manier :
log₅ 16 . log₈ 125
= log₅ 2⁴ . log₈ 5³
= (4.log₅ 2) . (3.log₈ 5)
= 12.log₈ 5 . log₅ 2
= 12.log₈ 2
= 12 . 1/3

= 4
2^de manier : met de Change Of Base formula
$\log_5 16 . \log_8 125 =\frac{\log_a 16}{\log_a 5}\cdot \frac{\log_a 125}{\log_a 8}=\frac{4.\log_a 2}{\log_a 5}\cdot \frac{3.\log_a 5}{3.\log_a 2}=4$