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Samenvatting Kwantitatieve methoden deel 2 - more maths
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Samenvatting van het vak kwantitatieve methoden (Lieven De Moor) THEORIE deel 2 - More Maths
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CH2: MORE MATHS1. SPECIALE VORMEN VAN VERGELIJKINGEN: LOGARITMEN
Waarom nodig?
• Vergelijkingen oplossen als 2x = 4 X+2
• Logaritme = tool om een macht te verwijderen
Hoe?
Net zoals we 25 = 32, kunnen we schrijven log2 32 = 5
Algemeen: x = bn is hetzelfde als logb x = n, waarbij
• B = base
• “log to the base b of x is n-
• b kan enkel positief zijn
Hoe logaritme uitwerken?
Tot welke macht moeten we de “base” verheffen om het getal uit te komen?
Voorbeeld:
Speciale gevallen
We kunnen het logaritme van elk positief getal uitwerken. Echter speciale gevallen:
• logb 1 = 0 (want b0 = 1)
• logb 0 = niet gedefinieerd (je kan geen macht verheffen op b om nul uit te komen)
• logb b = 1 (want b1 = b)
In de praktijk: meest voorkomende ‘bases’ = 10 en e (e = specifiek nummer: e = 2.7181281..)
• Logaritme van base 10: geschreven als log
• Logaritme van base e: geschreven als ln
è GRM
Rekenregels bij logaritmen
Log pq = log p + log q
Log (p/q) = log p – log q
Log pn = n log p
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