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

\({}^{3}\!\log(9)\)

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

a

\({}^{3}\!\log(9) = {}^{3}\!\log(3^{2}) = 2\)

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

\(\log(1\,000\,000)\)

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

c

\(\log(1\,000\,000) = \log(10^{6}) = 6\)

1p

1p

d

\({}^{4}\!\log(\frac{1}{16})\)

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

d

\({}^{4}\!\log(\frac{1}{16}) = {}^{4}\!\log(4^{-2}) = -2\)

1p

opgave 2

Bereken.

1p

a

\({}^{\frac{1}{5}}\!\log(\frac{1}{125})\)

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

a

\({}^{\frac{1}{5}}\!\log(\frac{1}{125}) = {}^{\frac{1}{5}}\!\log(\frac{1}{5}^{3}) = 3\)

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

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

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

c

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

1p

1p

d

\({}^{4}\!\log(4^{2{,}7})\)

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

d

\({}^{4}\!\log(4^{2{,}7}) = 2{,}7\)

1p

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