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Havo B 11.3 Machten en logaritmen. Logaritme en exponent 2 x = 8 x = 3 want 2 3 = 8 2 x = 8 ⇔ 2 log(8) 2 3 = 8 ⇔ 2 log(8) = 3 2 log(32) = 5 want 2 5 =

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Presentatie over: "Havo B 11.3 Machten en logaritmen. Logaritme en exponent 2 x = 8 x = 3 want 2 3 = 8 2 x = 8 ⇔ 2 log(8) 2 3 = 8 ⇔ 2 log(8) = 3 2 log(32) = 5 want 2 5 ="— Transcript van de presentatie:

1 havo B 11.3 Machten en logaritmen

2 Logaritme en exponent 2 x = 8 x = 3 want 2 3 = 8 2 x = 8 ⇔ 2 log(8) 2 3 = 8 ⇔ 2 log(8) = 3 2 log(32) = 5 want 2 5 = 32 algemeen: g log(x) = y betekent g y = x x > 0, g > 0 en g ≠ 1

3 Rekenregels voor logaritmen Uit g y = x en g log(x) = y volgt g g log(x) = x. g log(a) + g log(b) = g log(ab) g log(a) – g log(b) = g log( ) n · g log(a) = g log(a n ) g log(a) =

4 De standaardgrafiek y = g log(x) O x y 0 < g < 1 1 O x y g > 1 1 dalend stijgend domein bereik ℝ de y-as (x = 0) is asymptoot

5 opgave 49 af (x) = g (x) 2 log(6x) = log(x + 3) 2 log(6x) = 2 log(2) + 2 log(x + 3) 2 log(6x) = 2 log(2(x + 3) 2 log(6x) = 2 log(2x + 6) 6x = 2x + 6 4x = 6 x = 1½ voldoet snijpunt (1½, 2 log(9)) b O x y 1½1½ f g x = -3 f (x) ≤ g (x) 0 < x < 1½


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