Getal & Ruimte (12e editie) - havo wiskunde B

'Logaritmen herleiden'.

havo wiskunde B 9.3 Rekenregels voor logaritmen

Logaritmen herleiden (6)

opgave 1

Herleid tot één logaritme.

1p

a

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

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

a

\({}^{5}\!\log(2 x) + {}^{5}\!\log(3 x - 4)\)
\(\text{ } = {}^{5}\!\log(2 x ⋅ (3 x - 4))\)
\(\text{ } = {}^{5}\!\log(6 x^{2} - 8 x)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(2 ⋅ {}^{5}\!\log(4 x)\)

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

c

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

1p

○

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

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

○

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

1p

3p

b

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

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

b

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

1p

○

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

1p

○

\(\text{ } = {}^{5}\!\log(625 ⋅ (2 a - 1))\)
\(\text{ } = {}^{5}\!\log(1\,250 a - 625)\)

1p

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