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Samenvatting Wiskunde B HAVO Hoofdstuk 5 Machten, exponenten en logaritmen 2020 R45,69   Add to cart

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Samenvatting Wiskunde B HAVO Hoofdstuk 5 Machten, exponenten en logaritmen 2020

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Wiskunde B HAVO Hoofdstuk 5 Machten, exponenten en logaritmen 2020 PARAGRAAF 5.1 : MACHTEN EN WORTELS PARAGRAAF 5.2 : WORTELFORMULES PARAGRAAF 5.3 : EXPONENTIËLE FUNCTIES PARAGRAAF 5.4 : LOGARITMEN

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  • August 2, 2023
  • 14
  • 2020/2021
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Hoofdstuk 5 Machten, exponenten en logaritmen (H4 Wis B) Pagina 1 van 14



PARAGRAAF 5.1 : MACHTEN EN WORTELS




LES 1 : MACHTSREGELS



MACHTSREGELS VOORBEELD
(1) 𝑎𝑎𝑝𝑝 × 𝑎𝑎𝑞𝑞 = 𝑎𝑎𝑝𝑝+𝑞𝑞 𝑎𝑎3 × 𝑎𝑎5 = 𝑎𝑎3+5 = 𝑎𝑎8

𝑎𝑎 𝑝𝑝 𝑎𝑎 10
(2) 𝑎𝑎 𝑞𝑞
= 𝑎𝑎𝑝𝑝−𝑞𝑞 𝑎𝑎 2
= 𝑎𝑎10−2 = 𝑎𝑎8

(3) (𝑎𝑎𝑝𝑝 )𝑞𝑞 = 𝑎𝑎𝑝𝑝∙𝑞𝑞 (𝑎𝑎3 )4 = 𝑎𝑎3∙4 = 𝑎𝑎12

(4) (𝑎𝑎 ⋅ 𝑏𝑏)𝑝𝑝 = 𝑎𝑎𝑝𝑝 ⋅ 𝑏𝑏 𝑝𝑝 (𝑎𝑎 ⋅ 𝑏𝑏)3 = 𝑎𝑎3 ⋅ 𝑏𝑏 3

(5) 𝑎𝑎0 = 1 70 = 1
1 1
(6) 𝑎𝑎−𝑝𝑝 = 𝑎𝑎−3 =
𝑎𝑎 𝑝𝑝 𝑎𝑎 3

1 𝑛𝑛 1 3
(7) (𝑎𝑎)𝑛𝑛 = √𝑎𝑎 (𝑎𝑎)3 = √𝑎𝑎
𝑝𝑝 𝑛𝑛 3 5
(8) (𝑎𝑎)𝑛𝑛 = √𝑎𝑎𝑝𝑝 (𝑎𝑎)5 = √𝑎𝑎3




Er zijn ook twee speciale gevallen die vaak voorkomen

1 1 1 1
(9) 𝑎𝑎−1 = = 5−1 = =
𝑎𝑎 1 𝑎𝑎 51 5

2
(10) (𝑎𝑎)1/2 = 2√𝑎𝑎 = √𝑎𝑎 (6)1/2 = √6 = √6

, Hoofdstuk 5 Machten, exponenten en logaritmen (H4 Wis B) Pagina 2 van 14



VOORBEELD 1

Schrijf als macht van x

a. 𝑥𝑥 3 √𝑥𝑥
√𝑥𝑥
b. 𝑥𝑥
3 1
c. √𝑥𝑥 ∙ 2
𝑥𝑥


Schrijf zonder gebroken en negatieven machten
3
d. 𝑥𝑥 −4
1
e. 𝑥𝑥 −22



OPLOSSING 1
1 1
a. 𝑥𝑥 3 √𝑥𝑥 = 𝑥𝑥 3 ∙ 𝑥𝑥 2 = 𝑥𝑥 32
1
1 1
√𝑥𝑥 𝑥𝑥 2
b. 𝑥𝑥
= 𝑥𝑥 1 = 𝑥𝑥 2−1 = 𝑥𝑥 −2
1 2
1
c. √𝑥𝑥 ∙ 2 = 𝑥𝑥 3 ∙ 𝑥𝑥 −2 = 𝑥𝑥 −13
3
𝑥𝑥
3
1 1
d. 𝑥𝑥 −4 = 3 = 4
𝑥𝑥 4 √𝑥𝑥 3
1
1 1 1
e. 𝑥𝑥 −22 = 1 = 1 =
2 𝑥𝑥 2 √𝑥𝑥
𝑥𝑥 2 𝑥𝑥 2 ∙𝑥𝑥 2




VOORBEELD 2

Schrijf de volgende formules om in de vorm 𝑦𝑦 = 𝑎𝑎𝑥𝑥 𝑛𝑛 of 𝑦𝑦 = 𝑏𝑏𝑔𝑔 𝑥𝑥

1 2
a. 𝑦𝑦 = (2𝑥𝑥 −2 )3 4
4 𝑥𝑥
3𝑥𝑥+2
b. 𝑦𝑦 = 10 ∙ 2




OPLOSSING 2
1 2 1
a. 𝑦𝑦 = (2𝑥𝑥 −2 )3 𝑥𝑥 4 = ∙ 23 ∙ 𝑥𝑥 −6 ∙ 2 ∙ 𝑥𝑥 −4
4 4
1
𝑦𝑦 = ∙ 8 ∙ 2 ∙ 𝑥𝑥 ∙ 𝑥𝑥 −4 = 4𝑥𝑥 −10
−6
4
3𝑥𝑥+2 3𝑥𝑥 2
b. 𝑦𝑦 = 10 ∙ 2 = 10 ∙ 2 ∙2
𝑦𝑦 = 10 ∙ 22 ∙ (23 )𝑥𝑥 = 40 ∙ 8𝑥𝑥

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