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

\({}^{9}\!\log(81)\)

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

a

\({}^{9}\!\log(81) = {}^{9}\!\log(9^{2}) = 2\)

1p

1p

b

\({}^{8}\!\log(8)\)

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

b

\({}^{8}\!\log(8) = {}^{8}\!\log(8^{1}) = 1\)

1p

1p

c

\({}^{6}\!\log(\frac{1}{6})\)

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

c

\({}^{6}\!\log(\frac{1}{6}) = {}^{6}\!\log(6^{-1}) = -1\)

1p

1p

d

\({}^{\frac{1}{10}}\!\log(\frac{1}{100})\)

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

d

\({}^{\frac{1}{10}}\!\log(\frac{1}{100}) = {}^{\frac{1}{10}}\!\log(\frac{1}{10}^{2}) = 2\)

1p

opgave 2

Bereken.

1p

a

\({}^{\frac{1}{10}}\!\log(100)\)

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

a

\({}^{\frac{1}{10}}\!\log({}^{\frac{1}{10}}\!\log(100)) = {}^{\frac{1}{10}}\!\log(\frac{1}{10}^{-2}) = -2\)

1p

1p

b

\({}^{8}\!\log(8 \sqrt{8})\)

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

b

\({}^{8}\!\log(8 \sqrt{8}) = {}^{8}\!\log(8^{1} ⋅ 8^{\frac{1}{2}}) = {}^{8}\!\log(8^{1\frac{1}{2}}) = 1\frac{1}{2}\)

1p

1p

c

\({}^{8}\!\log(8^{1{,}9})\)

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

c

\({}^{8}\!\log(8^{1{,}9}) = 1{,}9\)

1p

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