Exam (elaborations)
Oefentoets moderne wiskunde H1 Havo 5
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Dit is het proefwerk van havo 5 H1 logaritmische functies
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Oefentoets H1 Logaritmische functies H5 WBRond eventueel af op twee decimalen.
1 Los de onderstaande vergelijkingen exact op.
(2) a. 4 + x 8=9
7
(3) b. 4 ∙ ❑log ( 2−x ) −3=5
c
(4) c. 2+3 ∙5 x =127 en geef je antwoord in de vorm x=a+ b ❑ log ( d )
6 6 6 6
(4) d. 2 ∙ ❑log ( 2 ) +2 ∙ ❑log ( 5+ x ) =❑log (1−x )+ ❑ log ( 4 )
1
2 Gegeven is de functie f ( x )=4+ 3∙ 2 log ( x−8 )
❑
(3) a. Geef exact het domein, bereik, asymptoot. Licht je antwoord toe.
(3) b. Bereken exact de snijpunten met de assen.
(5) c. Los exact op: f ( x)≥10 .
(3) d. Druk x uit in y.
3 Losse formules
2
(3) a. Herschrijf de formule g ( x )=❑4log ( 9 x )+ ❑2log (7 ) in de vorm g ( x )=❑log ( a x b ).
(3) b. Druk p uit in q.
4 q+1=5∙ ❑3log ( 4 p )
( )
6
P b
(3) c. Herschrijf naar de vorm q= log
❑ a
6 q=log ❑( 4 ) +¿ log ❑( p )−¿ ❑6 log ( 152 ) ¿ ¿
6 6
3
(3) d. Bereken het maximum van de formule n ( x )=1+2 ∙ ❑ log ( 5 x−4−x2 )
4 Voor de geluidsterkte D in decibel (dB) van een toongenerator geldt:
( )
❑ 5
4,9 ∙ 10
D=10 ∙ log 2
❑ r
Hierin is r de afstand in meters tot de generator.
(1) a. Bereken de geluidsterkte op een afstand van 25 meter.
(3) b. Bereken algebraïsch op welke afstand de geluidsterkte meer dan 36 dB is.
(3) c. De formule is te herleiden tot de vorm D=a+b ∙ log r .
Bereken de waarde van a en B
Einde van de toets
Normering onder voorbehoud
pnt
cijfer= ∗9+ 1
46
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