Getal & Ruimte (13e 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

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

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

a

\({}^{5}\!\log(3) + {}^{5}\!\log(2 a + 4)\)
\(\text{ } = {}^{5}\!\log(3 ⋅ (2 a + 4))\)
\(\text{ } = {}^{5}\!\log(6 a + 12)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(5 ⋅ {}^{2}\!\log(4 a)\)

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

c

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

1p

○

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

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(3 + {}^{2}\!\log(4 p - 1)\)
\(\text{ } = {}^{2}\!\log(2^{3}) + {}^{2}\!\log(4 p - 1)\)
\(\text{ } = {}^{2}\!\log(8) + {}^{2}\!\log(4 p - 1)\)

1p

○

\(\text{ } = {}^{2}\!\log(8 ⋅ (4 p - 1))\)
\(\text{ } = {}^{2}\!\log(32 p - 8)\)

1p

3p

b

\({}^{3}\!\log(9) + {}^{5}\!\log(4 a + 1)\)

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

b

\({}^{3}\!\log(9) + {}^{5}\!\log(4 a + 1)\)
\(\text{ } = {}^{3}\!\log(3^{2}) + {}^{5}\!\log(4 a + 1)\)
\(\text{ } = 2 + {}^{5}\!\log(4 a + 1)\)

1p

○

\(\text{ } = {}^{5}\!\log(5^{2}) + {}^{5}\!\log(4 a + 1)\)
\(\text{ } = {}^{5}\!\log(25) + {}^{5}\!\log(4 a + 1)\)

1p

○

\(\text{ } = {}^{5}\!\log(25 ⋅ (4 a + 1))\)
\(\text{ } = {}^{5}\!\log(100 a + 25)\)

1p

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