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

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

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

a

\({}^{5}\!\log(2) + {}^{5}\!\log(p - 4)\)
\(\text{ } = {}^{5}\!\log(2 ⋅ (p - 4))\)
\(\text{ } = {}^{5}\!\log(2 p - 8)\)

1p

1p

b

\({}^{3}\!\log(2) - {}^{3}\!\log(4 a - 1)\)

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

b

\({}^{3}\!\log(2) - {}^{3}\!\log(4 a - 1)\)
\(\text{ } = {}^{3}\!\log({2 \over 4 a - 1})\)

1p

2p

c

\(5 ⋅ {}^{4}\!\log(2 x)\)

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

c

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

1p

\(\text{ } = {}^{4}\!\log(32 x^{5})\)

1p

2p

d

\(4 ⋅ {}^{5}\!\log(x) + {}^{5}\!\log(2 x - 1)\)

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

d

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

1p

\(\text{ } = {}^{5}\!\log(x^{4} ⋅ (2 x - 1))\)
\(\text{ } = {}^{5}\!\log(2 x^{5} - x^{4})\)

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(3 + {}^{5}\!\log(2 a + 4)\)
\(\text{ } = {}^{5}\!\log(5^{3}) + {}^{5}\!\log(2 a + 4)\)
\(\text{ } = {}^{5}\!\log(125) + {}^{5}\!\log(2 a + 4)\)

1p

\(\text{ } = {}^{5}\!\log(125 ⋅ (2 a + 4))\)
\(\text{ } = {}^{5}\!\log(250 a + 500)\)

1p

3p

b

\({}^{2}\!\log(8) + {}^{4}\!\log(5 p - 1)\)

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

b

\({}^{2}\!\log(8) + {}^{4}\!\log(5 p - 1)\)
\(\text{ } = {}^{2}\!\log(2^{3}) + {}^{4}\!\log(5 p - 1)\)
\(\text{ } = 3 + {}^{4}\!\log(5 p - 1)\)

1p

\(\text{ } = {}^{4}\!\log(4^{3}) + {}^{4}\!\log(5 p - 1)\)
\(\text{ } = {}^{4}\!\log(64) + {}^{4}\!\log(5 p - 1)\)

1p

\(\text{ } = {}^{4}\!\log(64 ⋅ (5 p - 1))\)
\(\text{ } = {}^{4}\!\log(320 p - 64)\)

1p

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