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

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

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

a

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

1p

1p

b

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

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

b

\({}^{9}\!\log(1) = {}^{9}\!\log(9^{0}) = 0\)

1p

1p

c

\(\log(10)\)

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

c

\(\log(10) = \log(10^{1}) = 1\)

1p

1p

d

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

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

d

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

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

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

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

b

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

1p

1p

c

\({}^{8}\!\log(64 \sqrt{8})\)

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

c

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

1p

1p

d

\({}^{5}\!\log(5^{1{,}2})\)

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

d

\({}^{5}\!\log(5^{1{,}2}) = 1{,}2\)

1p

"