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

'Rekenen met logaritmen'.

havo wiskunde B 5.5 Logaritmen

Rekenen met logaritmen (8)

opgave 1

Bereken.

1p

a

\({}^{2}\!\log(32)\)

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

a

\({}^{2}\!\log(32) = {}^{2}\!\log(2^{5}) = 5\)

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

\(\log(10)\)

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

c

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

1p

1p

d

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

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

d

\({}^{2}\!\log(\frac{1}{64}) = {}^{2}\!\log(2^{-6}) = -6\)

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

\({}^{\frac{1}{4}}\!\log(64)\)

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

b

\({}^{\frac{1}{4}}\!\log({}^{\frac{1}{4}}\!\log(64)) = {}^{\frac{1}{4}}\!\log(\frac{1}{4}^{-3}) = -3\)

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

\({}^{7}\!\log(7^{6{,}2})\)

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

d

\({}^{7}\!\log(7^{6{,}2}) = 6{,}2\)

1p

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