Getal & Ruimte (12e editie) - vwo wiskunde A

'Rekenen met logaritmen'.

vwo wiskunde A 10.3 Logaritmen

Rekenen met logaritmen (8)

opgave 1

Bereken.

1p

a

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

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

a

\({}^{6}\!\log(36) = {}^{6}\!\log(6^{2}) = 2\)

1p

1p

b

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

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

b

\({}^{3}\!\log(1) = {}^{3}\!\log(3^{0}) = 0\)

1p

1p

c

\(\log(1\,000)\)

Logaritme (3)
00fk - Rekenen met logaritmen - basis - 0ms

c

\(\log(1\,000) = \log(10^{3}) = 3\)

1p

1p

d

\({}^{7}\!\log(\frac{1}{49})\)

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

d

\({}^{7}\!\log(\frac{1}{49}) = {}^{7}\!\log(7^{-2}) = -2\)

1p

opgave 2

Bereken.

1p

a

\({}^{\frac{1}{9}}\!\log(\frac{1}{81})\)

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

a

\({}^{\frac{1}{9}}\!\log(\frac{1}{81}) = {}^{\frac{1}{9}}\!\log(\frac{1}{9}^{2}) = 2\)

1p

1p

b

\({}^{\frac{1}{6}}\!\log(36)\)

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

b

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

1p

1p

c

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

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

c

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

1p

1p

d

\({}^{9}\!\log(9^{0{,}2})\)

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

d

\({}^{9}\!\log(9^{0{,}2}) = 0{,}2\)

1p

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