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

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

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

b

\({}^{8}\!\log(1) = {}^{8}\!\log(8^{0}) = 0\)

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

\({}^{3}\!\log(\frac{1}{3})\)

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

d

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

1p

opgave 2

Bereken.

1p

a

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

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

a

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

1p

1p

b

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

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

b

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

1p

1p

c

\({}^{5}\!\log(125 \sqrt{5})\)

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

c

\({}^{5}\!\log(125 \sqrt{5}) = {}^{5}\!\log(5^{3} ⋅ 5^{\frac{1}{2}}) = {}^{5}\!\log(5^{3\frac{1}{2}}) = 3\frac{1}{2}\)

1p

1p

d

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

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

d

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

1p

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