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Samenvatting Exponentiële en logaritmische functies $3.25   Add to cart
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Samenvatting Exponentiële en logaritmische functies
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  • Course
  • Wiskunde B
  • Level
  • VWO / Gymnasium

Dit is een samenvatting van wiskunde B uit vwo 5. De onderwerpen die aan bod komen, zijn: log functie, Ln, afgeleide van Ln, translaties, verticale lijnstukken, horizontale lijnstukken, verhouding van lijnstukken en voorbeeld van rekenen aan log functies.

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Document information

  • February 5, 2018
  • 3
  • 2015/2016
  • Summary

Subjects

  • log functie
  • afgeleide van ln
  • translaties
  • verticale lijnstukken
  • horizontale lijnstukken
  • ln
  • verhouding van lijnstukken

Written for

  • Secondary school
  • VWO / Gymnasium
  • Wiskunde B
  • 5
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𝐥𝐨𝐠 functie
𝐥𝐨𝐠𝒂 𝒃 = 𝒄 want 𝒂𝒄 = 𝒃 dus log4 16 = 2

𝐥𝐨𝐠𝒂 𝒂𝒄 = 𝒄 dat komt ook terug in log4 42 = 2

𝐥𝐨𝐠𝒈 𝒂 + 𝐥𝐨𝐠𝒈 𝒃 = 𝐥𝐨𝐠𝒈 (𝒂 ∙ 𝒃) dus log10 10 + log10 100 = log10(10 ∙ 100) = log10 1000 = 3

𝒏 ∙ 𝐥𝐨𝐠 𝒈 𝒂 = 𝐥𝐨𝐠 𝒈 𝒂𝒏 want log𝑔 𝑎 + log𝑔 𝑎 + log𝑔 𝑎 = log𝑔 𝑎3

𝒂 12
𝐥𝐨𝐠 𝒈 𝒂 − 𝐥𝐨𝐠 𝒈 𝒃 = 𝐥𝐨𝐠 𝒈 (𝒃) dus log 2 12 − log 2 3 = log 2 ( 3 ) = log 2 4 = log 2 22 = 2

𝐥𝐨𝐠𝒈 𝒂 = 𝐥𝐨𝐠𝒈 𝒃 → 𝒂 = 𝒃

𝐥𝐨𝐠 = 𝐥𝐨𝐠 𝟏𝟎

𝐥𝐨𝐠 𝒑 𝒂 log3 𝑥 log3 𝑥
𝐥𝐨𝐠 𝒈 𝒂 = 𝐥𝐨𝐠 p kan hier elke waarde hebben die je wil: log 1 𝑥 = 1 = log −1
= −log 3 𝑥
𝒑𝒈 3 log3 ( ) 3 (3 )
3


𝐥𝐨𝐠 𝟏 𝒂 = −𝐥𝐨𝐠 𝒈 𝒂
𝒈


𝐥𝐨𝐠 𝒑 𝒙 = 𝟎 → 𝒙 = 𝟏 want p0=1, maakt niet uit welk getal ‘p’ is

𝒂𝐥𝐨𝐠𝒂 𝒃 = 𝒃

𝐥𝐨𝐠 𝒆 𝒂 = 𝑳𝒏 𝒂 dus 𝐿𝑛 𝑒 2 = 2

𝐥𝐨𝐠 𝒈 𝟎, kan niet, maakt niet uit welk getal g is

Afgeleide van 𝑳𝒏
𝟏
[𝑳𝒏(𝒙)]′ =
𝒙

𝟏
[𝐥𝐨𝐠 𝒂 𝒙]′ =
𝒙 ∙ 𝑳𝒏(𝒂)

[𝒆𝒙 ]′ = 𝒆𝒙

[𝟐𝒙 ]′ = 𝟐𝒙 ∙ 𝑳𝒏(𝟐) dus [34𝑥−2 ]′ = 34𝑥−2 ∙ 4 ∙ 𝐿𝑛(3)

Translaties
De translatie (3,0) houdt in dat de hele formule 3 naar rechts gaat dat vul je in de formule in als x-3
bv: 2𝑥 → 2𝑥−3 (als je naar links wil moet je x+3 ervan maken)
De translatie (0,1) houdt in dat de hele formule 1 omhoog gaat dat vul je in de formule in als:
𝑓(𝑥) → 𝑓(𝑥) + 1
Vermenigvuldig de x-as met 3, dan vermenigvuldig je de hele formule met 3:
𝑓(𝑥) → 3 ∙ 𝑓(𝑥)
𝑥
Vermenigvuldig de y-as met 2, dan moet je alle x’en vervangen door 2 dus:

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