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havo B 11.3 Machten en logaritmen
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Logaritme en exponent 2x = 8 x = 3 want 23 = 8 2x = 8 ⇔ 2log(8)
2log(32) = 5 want 25 = 32 algemeen: glog(x) = y betekent gy = x x > 0 , g > 0 en g ≠ 1
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Rekenregels voor logaritmen
Uit gy = x en glog(x) = y volgt gglog(x) = x. glog(a) + glog(b) = glog(ab) glog(a) – glog(b) = glog( ) n · glog(a) = glog(an) glog(a) =
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De standaardgrafiek y = glog(x)
1 1 dalend stijgend domein < 0, > bereik ℝ de y-as (x = 0) is asymptoot
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2log(6x) = 2log(2) + 2log(x + 3) 2log(6x) = 2log(2(x + 3)
opgave 49 y b x = -3 a f (x) = g (x) 2log(6x) = 1 + 2log(x + 3) 2log(6x) = 2log(2) + 2log(x + 3) 2log(6x) = 2log(2(x + 3) 2log(6x) = 2log(2x + 6) 6x = 2x + 6 4x = 6 x = 1½ voldoet snijpunt (1½, 2log(9)) f g x O 1½ f (x) ≤ g (x) 0 < x < 1½
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