Getal & Ruimte (13e editie) - havo wiskunde B

'Rekenen met logaritmen'.

havo wiskunde B 5.5 Logaritmen

Rekenen met logaritmen (7)

opgave 1

Bereken.

1p

a

\({}^{7}\!\log(49)\)

Logaritme (1)
00fi - Rekenen met logaritmen - basis - 0ms

a

\({}^{7}\!\log(49) = {}^{7}\!\log(7^{2}) = 2\)

1p

1p

b

\({}^{5}\!\log(5)\)

Logaritme (2)
00fj - Rekenen met logaritmen - basis - 0ms

b

\({}^{5}\!\log(5) = {}^{5}\!\log(5^{1}) = 1\)

1p

1p

c

\({}^{2}\!\log(\frac{1}{4})\)

Logaritme (4)
00fl - Rekenen met logaritmen - basis - 0ms

c

\({}^{2}\!\log(\frac{1}{4}) = {}^{2}\!\log(2^{-2}) = -2\)

1p

1p

d

\({}^{\frac{1}{3}}\!\log(\frac{1}{27})\)

Logaritme (5)
00fm - Rekenen met logaritmen - basis - 0ms

d

\({}^{\frac{1}{3}}\!\log(\frac{1}{27}) = {}^{\frac{1}{3}}\!\log(\frac{1}{3}^{3}) = 3\)

1p

opgave 2

Bereken.

1p

a

\({}^{\frac{1}{3}}\!\log(9)\)

Logaritme (6)
00fn - Rekenen met logaritmen - basis - 0ms

a

\({}^{\frac{1}{3}}\!\log({}^{\frac{1}{3}}\!\log(9)) = {}^{\frac{1}{3}}\!\log(\frac{1}{3}^{-2}) = -2\)

1p

1p

b

\({}^{6}\!\log(36 \sqrt{6})\)

Logaritme (7)
00fo - Rekenen met logaritmen - basis - 0ms

b

\({}^{6}\!\log(36 \sqrt{6}) = {}^{6}\!\log(6^{2} ⋅ 6^{\frac{1}{2}}) = {}^{6}\!\log(6^{2\frac{1}{2}}) = 2\frac{1}{2}\)

1p

1p

c

\({}^{3}\!\log(3^{2{,}8})\)

Logaritme (8)
00fp - Rekenen met logaritmen - basis - 0ms

c

\({}^{3}\!\log(3^{2{,}8}) = 2{,}8\)

1p

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