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

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

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

a

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

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

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

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

c

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

1p

1p

d

\({}^{2}\!\log(\frac{1}{32})\)

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

d

\({}^{2}\!\log(\frac{1}{32}) = {}^{2}\!\log(2^{-5}) = -5\)

1p

opgave 2

Bereken.

1p

a

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

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

a

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

1p

1p

b

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

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

b

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

1p

1p

c

\({}^{4}\!\log(64 \sqrt{4})\)

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

c

\({}^{4}\!\log(64 \sqrt{4}) = {}^{4}\!\log(4^{3} ⋅ 4^{\frac{1}{2}}) = {}^{4}\!\log(4^{3\frac{1}{2}}) = 3\frac{1}{2}\)

1p

1p

d

\({}^{4}\!\log(4^{2{,}1})\)

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

d

\({}^{4}\!\log(4^{2{,}1}) = 2{,}1\)

1p

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