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

'Logaritmen herleiden'.

havo wiskunde B 9.3 Rekenregels voor logaritmen

Logaritmen herleiden (6)

opgave 1

Herleid tot één logaritme.

1p

a

\({}^{5}\!\log(a) + {}^{5}\!\log(4 a + 2)\)

Optellen (1)
00ku - Logaritmen herleiden - basis - basis - 0ms - dynamic variables

a

\({}^{5}\!\log(a) + {}^{5}\!\log(4 a + 2)\)
\(\text{ } = {}^{5}\!\log(a ⋅ (4 a + 2))\)
\(\text{ } = {}^{5}\!\log(4 a^{2} + 2 a)\)

1p

1p

b

\({}^{5}\!\log(2 p) - {}^{5}\!\log(4 p - 1)\)

Aftrekken
00kv - Logaritmen herleiden - basis - eind - 0ms - dynamic variables

b

\({}^{5}\!\log(2 p) - {}^{5}\!\log(4 p - 1)\)
\(\text{ } = {}^{5}\!\log({2 p \over 4 p - 1})\)

1p

2p

c

\(5 ⋅ {}^{2}\!\log(4 a)\)

Vermenigvuldigen
00kw - Logaritmen herleiden - basis - midden - 1ms - dynamic variables

c

\(5 ⋅ {}^{2}\!\log(4 a)\)
\(\text{ } = {}^{2}\!\log((4 a)^{5})\)

1p

○

\(\text{ } = {}^{2}\!\log(1\,024 a^{5})\)

1p

2p

d

\(2 ⋅ {}^{3}\!\log(x) + {}^{3}\!\log(4 x - 5)\)

OptellenVermenigvuldigen
00kx - Logaritmen herleiden - basis - eind - 0ms - dynamic variables

d

\(2 ⋅ {}^{3}\!\log(x) + {}^{3}\!\log(4 x - 5)\)
\(\text{ } = {}^{3}\!\log(x^{2}) + {}^{3}\!\log(4 x - 5)\)

1p

○

\(\text{ } = {}^{3}\!\log(x^{2} ⋅ (4 x - 5))\)
\(\text{ } = {}^{3}\!\log(4 x^{3} - 5 x^{2})\)

1p

opgave 2

Herleid tot één logaritme.

2p

a

\(4 + {}^{3}\!\log(2 x - 5)\)

Grondtal (1)
00ky - Logaritmen herleiden - basis - midden - 0ms - dynamic variables

a

\(4 + {}^{3}\!\log(2 x - 5)\)
\(\text{ } = {}^{3}\!\log(3^{4}) + {}^{3}\!\log(2 x - 5)\)
\(\text{ } = {}^{3}\!\log(81) + {}^{3}\!\log(2 x - 5)\)

1p

○

\(\text{ } = {}^{3}\!\log(81 ⋅ (2 x - 5))\)
\(\text{ } = {}^{3}\!\log(162 x - 405)\)

1p

3p

b

\({}^{2}\!\log(16) + {}^{3}\!\log(5 x + 1)\)

Grondtal (2)
00kz - Logaritmen herleiden - basis - eind - 0ms - dynamic variables

b

\({}^{2}\!\log(16) + {}^{3}\!\log(5 x + 1)\)
\(\text{ } = {}^{2}\!\log(2^{4}) + {}^{3}\!\log(5 x + 1)\)
\(\text{ } = 4 + {}^{3}\!\log(5 x + 1)\)

1p

○

\(\text{ } = {}^{3}\!\log(3^{4}) + {}^{3}\!\log(5 x + 1)\)
\(\text{ } = {}^{3}\!\log(81) + {}^{3}\!\log(5 x + 1)\)

1p

○

\(\text{ } = {}^{3}\!\log(81 ⋅ (5 x + 1))\)
\(\text{ } = {}^{3}\!\log(405 x + 81)\)

1p

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