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

\({}^{4}\!\log(16)\)

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

a

\({}^{4}\!\log(16) = {}^{4}\!\log(4^{2}) = 2\)

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

\(\log(100\,000)\)

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

c

\(\log(100\,000) = \log(10^{5}) = 5\)

1p

1p

d

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

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

d

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

1p

opgave 2

Bereken.

1p

a

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

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

a

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

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

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

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

c

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

1p

1p

d

\({}^{8}\!\log(8^{4{,}7})\)

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

d

\({}^{8}\!\log(8^{4{,}7}) = 4{,}7\)

1p

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