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

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

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

a

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

1p

1p

b

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

Logaritme (2)
00fj - Rekenen met logaritmen - basis - 0ms

b

\({}^{5}\!\log(1) = {}^{5}\!\log(5^{0}) = 0\)

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

\({}^{7}\!\log(\frac{1}{49})\)

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

d

\({}^{7}\!\log(\frac{1}{49}) = {}^{7}\!\log(7^{-2}) = -2\)

1p

opgave 2

Bereken.

1p

a

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

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

a

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

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

\({}^{7}\!\log(7^{3{,}3})\)

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

d

\({}^{7}\!\log(7^{3{,}3}) = 3{,}3\)

1p

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