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

\({}^{5}\!\log(25)\)

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

a

\({}^{5}\!\log(25) = {}^{5}\!\log(5^{2}) = 2\)

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

\(\log(100)\)

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

c

\(\log(100) = \log(10^{2}) = 2\)

1p

1p

d

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

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

d

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

1p

opgave 2

Bereken.

1p

a

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

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

a

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

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

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

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

c

\({}^{2}\!\log(8 \sqrt{2}) = {}^{2}\!\log(2^{3} ⋅ 2^{\frac{1}{2}}) = {}^{2}\!\log(2^{3\frac{1}{2}}) = 3\frac{1}{2}\)

1p

1p

d

\({}^{2}\!\log(2^{6{,}5})\)

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

d

\({}^{2}\!\log(2^{6{,}5}) = 6{,}5\)

1p

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