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

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

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

a

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

1p

1p

b

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

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

b

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

1p

2p

c

\(2 ⋅ {}^{3}\!\log(4 x)\)

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

c

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

1p

\(\text{ } = {}^{3}\!\log(16 x^{2})\)

1p

2p

d

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

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

d

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

1p

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(2 + {}^{4}\!\log(3 a - 5)\)
\(\text{ } = {}^{4}\!\log(4^{2}) + {}^{4}\!\log(3 a - 5)\)
\(\text{ } = {}^{4}\!\log(16) + {}^{4}\!\log(3 a - 5)\)

1p

\(\text{ } = {}^{4}\!\log(16 ⋅ (3 a - 5))\)
\(\text{ } = {}^{4}\!\log(48 a - 80)\)

1p

3p

b

\({}^{2}\!\log(32) + {}^{4}\!\log(3 p - 1)\)

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

b

\({}^{2}\!\log(32) + {}^{4}\!\log(3 p - 1)\)
\(\text{ } = {}^{2}\!\log(2^{5}) + {}^{4}\!\log(3 p - 1)\)
\(\text{ } = 5 + {}^{4}\!\log(3 p - 1)\)

1p

\(\text{ } = {}^{4}\!\log(4^{5}) + {}^{4}\!\log(3 p - 1)\)
\(\text{ } = {}^{4}\!\log(1\,024) + {}^{4}\!\log(3 p - 1)\)

1p

\(\text{ } = {}^{4}\!\log(1\,024 ⋅ (3 p - 1))\)
\(\text{ } = {}^{4}\!\log(3\,072 p - 1\,024)\)

1p

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