Getal & Ruimte (13e editie) - havo wiskunde B

'Rekenen met logaritmen'.

havo wiskunde B 5.5 Logaritmen

Rekenen met logaritmen (7)

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

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

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

b

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

1p

1p

c

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

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

c

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

1p

1p

d

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

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

d

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

1p

opgave 2

Bereken.

1p

a

\({}^{\frac{1}{5}}\!\log(25)\)

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

a

\({}^{\frac{1}{5}}\!\log({}^{\frac{1}{5}}\!\log(25)) = {}^{\frac{1}{5}}\!\log(\frac{1}{5}^{-2}) = -2\)

1p

1p

b

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

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

b

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

1p

1p

c

\({}^{2}\!\log(2^{0{,}7})\)

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

c

\({}^{2}\!\log(2^{0{,}7}) = 0{,}7\)

1p

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