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

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

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

a

\({}^{3}\!\log(5 a) + {}^{3}\!\log(4 a + 2)\)
\(\text{ } = {}^{3}\!\log(5 a ⋅ (4 a + 2))\)
\(\text{ } = {}^{3}\!\log(20 a^{2} + 10 a)\)

1p

1p

b

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

Aftrekken
00kv - Logaritmen herleiden - basis - eind - 0ms - dynamic variables

b

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

1p

2p

c

\(3 ⋅ {}^{5}\!\log(2 a)\)

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

c

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

1p

○

\(\text{ } = {}^{5}\!\log(8 a^{3})\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

○

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

1p

3p

b

\({}^{5}\!\log(25) + {}^{4}\!\log(a - 3)\)

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

b

\({}^{5}\!\log(25) + {}^{4}\!\log(a - 3)\)
\(\text{ } = {}^{5}\!\log(5^{2}) + {}^{4}\!\log(a - 3)\)
\(\text{ } = 2 + {}^{4}\!\log(a - 3)\)

1p

○

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

1p

○

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

1p

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