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

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

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

a

\({}^{3}\!\log(4) + {}^{3}\!\log(5 x + 2)\)
\(\text{ } = {}^{3}\!\log(4 ⋅ (5 x + 2))\)
\(\text{ } = {}^{3}\!\log(20 x + 8)\)

1p

1p

b

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

Aftrekken
00kv - Logaritmen herleiden - basis - eind - 1ms - dynamic variables

b

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

1p

2p

c

\(3 ⋅ {}^{4}\!\log(2 x)\)

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

c

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

1p

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

1p

2p

d

\(5 ⋅ {}^{3}\!\log(p) + {}^{3}\!\log(4 p - 1)\)

OptellenVermenigvuldigen
00kx - Logaritmen herleiden - basis - eind - 1ms - dynamic variables

d

\(5 ⋅ {}^{3}\!\log(p) + {}^{3}\!\log(4 p - 1)\)
\(\text{ } = {}^{3}\!\log(p^{5}) + {}^{3}\!\log(4 p - 1)\)

1p

\(\text{ } = {}^{3}\!\log(p^{5} ⋅ (4 p - 1))\)
\(\text{ } = {}^{3}\!\log(4 p^{6} - p^{5})\)

1p

opgave 2

Herleid tot één logaritme.

2p

a

\(4 + {}^{2}\!\log(a + 3)\)

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

a

\(4 + {}^{2}\!\log(a + 3)\)
\(\text{ } = {}^{2}\!\log(2^{4}) + {}^{2}\!\log(a + 3)\)
\(\text{ } = {}^{2}\!\log(16) + {}^{2}\!\log(a + 3)\)

1p

\(\text{ } = {}^{2}\!\log(16 ⋅ (a + 3))\)
\(\text{ } = {}^{2}\!\log(16 a + 48)\)

1p

3p

b

\({}^{5}\!\log(625) + {}^{3}\!\log(x - 2)\)

Grondtal (2)
00kz - Logaritmen herleiden - basis - eind - 1ms - dynamic variables

b

\({}^{5}\!\log(625) + {}^{3}\!\log(x - 2)\)
\(\text{ } = {}^{5}\!\log(5^{4}) + {}^{3}\!\log(x - 2)\)
\(\text{ } = 4 + {}^{3}\!\log(x - 2)\)

1p

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

1p

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

1p

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