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Samenvatting Hoofdstuk 12 logaritmische functies - Wiskunde A $7.52
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Samenvatting Hoofdstuk 12 logaritmische functies - Wiskunde A
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  • Course
  • Wiskunde A
  • Level
  • VWO / Gymnasium

Deze samenvatting van hoofdstuk 12: logaritmische functies bevat onderwerpen zoals logaritmes, grondtal, verdubbelingstijd, halveringstijd, grafieken van logaritmische functies, rekenregels voor logaritmen en formules van logaritmische functies herleiden.

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Document information

  • April 9, 2024
  • 3
  • 2023/2024
  • Summary

Subjects

  • logaritmische functies
  • logaritme
  • grondtal
  • verdubbelingstijd
  • halveringstijd
  • formules herleiden
  • grafieken van logaritmische functies
  • rekenregels voor logaritmen
  • logaritmische schaalverdeling

Written for

  • Secondary school
  • VWO / Gymnasium
  • Wiskunde A
  • 5
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HOOFDSTUK 12 – LOGARITMISCHE
FUNCTIES
VOORKENNIS
Rekenregels:
g =1 met g ≠ 0
o p q p−q
g ∕ g =g
−p 1
g = P met ( g ≠ 0 ) q
( g p ) =g p ⋅ q
g
1
g p = √ g met ( g ≥ 0 ) g p ⋅ gq=g p+q
p



g = groeifactor pet tijdseenheid
groeifactor per n tijdseenheden = gn
1
groeifactor n-de deel = g n = √n g

PARAGRAAF 1 – LOGARITMEN
t
g =a , oplossing van vergelijking

Logaritme van a met grondtal g
Uit gt =a komt t=¿ glog(a) en andersom
Hierbij a> 0, g>0 , g ≠1

Voorbeeld 1 Voorbeeld 1
Los op: 6t-2=19 Los op: 4t=13
Oplossing: Oplossing:
6t-2=19  t-2=6log(19) 4t=13  t=4log(13)≈
t=6log(19)+2


PARAGRAAF 2 – LOGARITMEN BEREKENEN

Log(100) = 10
log(100)

Voorbeeld
Los op: 10t=50
Oplossing:
t=log(5)≈ 1,70

log ( a )
Rekenregel: glog(a)=
log ( g )

Voorbeeld 1 Voorbeeld 2
5t+1=23 Bereken 7log(4) in 2
Geef exacte vergelijking en met 2 decimalen
decimalen Oplossing:
Oplossing: log ( 4 )
5t+1=23  t+1=5log(23)
7
log(4) = ≈ 0.71
Exact = t = 5log(23)-1 log ( 7 )
log ( 23 )
2 decimalen = t - −1 ≈ 0,95
log ( 5 )

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