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

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

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

a

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

1p

1p

b

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

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

b

\({}^{7}\!\log(1) = {}^{7}\!\log(7^{0}) = 0\)

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

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

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

d

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

1p

opgave 2

Bereken.

1p

a

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

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

a

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

1p

1p

b

\({}^{\frac{1}{8}}\!\log(64)\)

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

b

\({}^{\frac{1}{8}}\!\log({}^{\frac{1}{8}}\!\log(64)) = {}^{\frac{1}{8}}\!\log(\frac{1}{8}^{-2}) = -2\)

1p

1p

c

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

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

c

\({}^{3}\!\log(3 \sqrt{3}) = {}^{3}\!\log(3^{1} ⋅ 3^{\frac{1}{2}}) = {}^{3}\!\log(3^{1\frac{1}{2}}) = 1\frac{1}{2}\)

1p

1p

d

\({}^{2}\!\log(2^{8{,}9})\)

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

d

\({}^{2}\!\log(2^{8{,}9}) = 8{,}9\)

1p

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