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

'Rekenen met logaritmen'.

vwo wiskunde B 5.4 Logaritmen

Rekenen met logaritmen (8)

opgave 1

Bereken.

1p

a

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

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

a

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

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

\(\log(10)\)

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

c

\(\log(10) = \log(10^{1}) = 1\)

1p

1p

d

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

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

d

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

1p

opgave 2

Bereken.

1p

a

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

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

a

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

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

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

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

c

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

1p

1p

d

\({}^{4}\!\log(4^{7{,}9})\)

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

d

\({}^{4}\!\log(4^{7{,}9}) = 7{,}9\)

1p

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