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

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

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

a

\({}^{5}\!\log(4) + {}^{5}\!\log(3 a + 2)\)
\(\text{ } = {}^{5}\!\log(4 ⋅ (3 a + 2))\)
\(\text{ } = {}^{5}\!\log(12 a + 8)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(5 ⋅ {}^{2}\!\log(4 x)\)

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

c

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

1p

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

1p

2p

d

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

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

d

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

1p

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

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

1p

3p

b

\({}^{5}\!\log(625) + {}^{3}\!\log(2 x + 1)\)

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

b

\({}^{5}\!\log(625) + {}^{3}\!\log(2 x + 1)\)
\(\text{ } = {}^{5}\!\log(5^{4}) + {}^{3}\!\log(2 x + 1)\)
\(\text{ } = 4 + {}^{3}\!\log(2 x + 1)\)

1p

\(\text{ } = {}^{3}\!\log(3^{4}) + {}^{3}\!\log(2 x + 1)\)
\(\text{ } = {}^{3}\!\log(81) + {}^{3}\!\log(2 x + 1)\)

1p

\(\text{ } = {}^{3}\!\log(81 ⋅ (2 x + 1))\)
\(\text{ } = {}^{3}\!\log(162 x + 81)\)

1p

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