100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Samenvatting Wiskunde B HAVO Hoofdstuk 5 Machten, exponenten en logaritmen 2020 $2.55
Add to cart
Quickly navigate to
Preview
  2.  
  3. Mathematics
  4.  
  5. Mathematics
  6.  
  7. Mathematics

Summary

Samenvatting Wiskunde B HAVO Hoofdstuk 5 Machten, exponenten en logaritmen 2020
 0 purchase
  • Course
  • Mathematics
  • Institution
  • Mathematics

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

Preview 2 out of 14  pages

Document information

  • August 2, 2023
  • 14
  • 2020/2021
  • Summary

Subjects

  • wiskunde b havo

Written for

  • Mathematics
All documents for this subject (937)

Seller

avatar-seller
tandhiwahyono

Reviews received

Content preview

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

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller tandhiwahyono. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $2.55. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

69252 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 15 years now

Start selling
$2.55
  • (0)
Add to cart
Added