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

\({}^{4}\!\log(64)\)

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

a

\({}^{4}\!\log(64) = {}^{4}\!\log(4^{3}) = 3\)

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

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

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

c

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

1p

1p

d

\({}^{\frac{1}{3}}\!\log(\frac{1}{27})\)

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

d

\({}^{\frac{1}{3}}\!\log(\frac{1}{27}) = {}^{\frac{1}{3}}\!\log(\frac{1}{3}^{3}) = 3\)

1p

opgave 2

Bereken.

1p

a

\({}^{\frac{1}{10}}\!\log(100)\)

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

a

\({}^{\frac{1}{10}}\!\log({}^{\frac{1}{10}}\!\log(100)) = {}^{\frac{1}{10}}\!\log(\frac{1}{10}^{-2}) = -2\)

1p

1p

b

\({}^{7}\!\log(7 \sqrt{7})\)

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

b

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

1p

1p

c

\({}^{8}\!\log(8^{4{,}3})\)

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

c

\({}^{8}\!\log(8^{4{,}3}) = 4{,}3\)

1p

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