Getal & Ruimte (12e editie) - vwo wiskunde B

'Logaritmen herleiden'.

vwo wiskunde B 9.1 Rekenregels voor logaritmen

Logaritmen herleiden (6)

opgave 1

Herleid tot één logaritme.

1p

a

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

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

a

\({}^{4}\!\log(5) + {}^{4}\!\log(2 x - 3)\)
\(\text{ } = {}^{4}\!\log(5 ⋅ (2 x - 3))\)
\(\text{ } = {}^{4}\!\log(10 x - 15)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(3 ⋅ {}^{2}\!\log(5 a)\)

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

c

\(3 ⋅ {}^{2}\!\log(5 a)\)
\(\text{ } = {}^{2}\!\log((5 a)^{3})\)

1p

○

\(\text{ } = {}^{2}\!\log(125 a^{3})\)

1p

2p

d

\(5 ⋅ {}^{2}\!\log(a) + {}^{2}\!\log(3 a - 1)\)

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

d

\(5 ⋅ {}^{2}\!\log(a) + {}^{2}\!\log(3 a - 1)\)
\(\text{ } = {}^{2}\!\log(a^{5}) + {}^{2}\!\log(3 a - 1)\)

1p

○

\(\text{ } = {}^{2}\!\log(a^{5} ⋅ (3 a - 1))\)
\(\text{ } = {}^{2}\!\log(3 a^{6} - a^{5})\)

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(2 + {}^{3}\!\log(5 x - 4)\)
\(\text{ } = {}^{3}\!\log(3^{2}) + {}^{3}\!\log(5 x - 4)\)
\(\text{ } = {}^{3}\!\log(9) + {}^{3}\!\log(5 x - 4)\)

1p

○

\(\text{ } = {}^{3}\!\log(9 ⋅ (5 x - 4))\)
\(\text{ } = {}^{3}\!\log(45 x - 36)\)

1p

3p

b

\({}^{2}\!\log(8) + {}^{4}\!\log(a + 5)\)

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

b

\({}^{2}\!\log(8) + {}^{4}\!\log(a + 5)\)
\(\text{ } = {}^{2}\!\log(2^{3}) + {}^{4}\!\log(a + 5)\)
\(\text{ } = 3 + {}^{4}\!\log(a + 5)\)

1p

○

\(\text{ } = {}^{4}\!\log(4^{3}) + {}^{4}\!\log(a + 5)\)
\(\text{ } = {}^{4}\!\log(64) + {}^{4}\!\log(a + 5)\)

1p

○

\(\text{ } = {}^{4}\!\log(64 ⋅ (a + 5))\)
\(\text{ } = {}^{4}\!\log(64 a + 320)\)

1p

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