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

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

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

a

\({}^{2}\!\log(5 a) + {}^{2}\!\log(3 a + 1)\)
\(\text{ } = {}^{2}\!\log(5 a ⋅ (3 a + 1))\)
\(\text{ } = {}^{2}\!\log(15 a^{2} + 5 a)\)

1p

1p

b

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

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

b

\({}^{3}\!\log(2 x) - {}^{3}\!\log(4 x - 1)\)
\(\text{ } = {}^{3}\!\log({2 x \over 4 x - 1})\)

1p

2p

c

\(4 ⋅ {}^{3}\!\log(5 p)\)

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

c

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

1p

\(\text{ } = {}^{3}\!\log(625 p^{4})\)

1p

2p

d

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

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

d

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

1p

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(5 + {}^{4}\!\log(3 a + 2)\)
\(\text{ } = {}^{4}\!\log(4^{5}) + {}^{4}\!\log(3 a + 2)\)
\(\text{ } = {}^{4}\!\log(1\,024) + {}^{4}\!\log(3 a + 2)\)

1p

\(\text{ } = {}^{4}\!\log(1\,024 ⋅ (3 a + 2))\)
\(\text{ } = {}^{4}\!\log(3\,072 a + 2\,048)\)

1p

3p

b

\({}^{4}\!\log(1\,024) + {}^{3}\!\log(2 x - 1)\)

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

b

\({}^{4}\!\log(1\,024) + {}^{3}\!\log(2 x - 1)\)
\(\text{ } = {}^{4}\!\log(4^{5}) + {}^{3}\!\log(2 x - 1)\)
\(\text{ } = 5 + {}^{3}\!\log(2 x - 1)\)

1p

\(\text{ } = {}^{3}\!\log(3^{5}) + {}^{3}\!\log(2 x - 1)\)
\(\text{ } = {}^{3}\!\log(243) + {}^{3}\!\log(2 x - 1)\)

1p

\(\text{ } = {}^{3}\!\log(243 ⋅ (2 x - 1))\)
\(\text{ } = {}^{3}\!\log(486 x - 243)\)

1p

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