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

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

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

a

\({}^{4}\!\log(3) + {}^{4}\!\log(2 x + 5)\)
\(\text{ } = {}^{4}\!\log(3 ⋅ (2 x + 5))\)
\(\text{ } = {}^{4}\!\log(6 x + 15)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(3 ⋅ {}^{4}\!\log(5 a)\)

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

c

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

1p

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

1p

2p

d

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

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

d

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

1p

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(3 + {}^{5}\!\log(2 p + 1)\)
\(\text{ } = {}^{5}\!\log(5^{3}) + {}^{5}\!\log(2 p + 1)\)
\(\text{ } = {}^{5}\!\log(125) + {}^{5}\!\log(2 p + 1)\)

1p

\(\text{ } = {}^{5}\!\log(125 ⋅ (2 p + 1))\)
\(\text{ } = {}^{5}\!\log(250 p + 125)\)

1p

3p

b

\({}^{3}\!\log(81) + {}^{2}\!\log(5 x + 1)\)

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

b

\({}^{3}\!\log(81) + {}^{2}\!\log(5 x + 1)\)
\(\text{ } = {}^{3}\!\log(3^{4}) + {}^{2}\!\log(5 x + 1)\)
\(\text{ } = 4 + {}^{2}\!\log(5 x + 1)\)

1p

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

1p

\(\text{ } = {}^{2}\!\log(16 ⋅ (5 x + 1))\)
\(\text{ } = {}^{2}\!\log(80 x + 16)\)

1p

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