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

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

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

a

\({}^{2}\!\log(5) + {}^{2}\!\log(4 p + 1)\)
\(\text{ } = {}^{2}\!\log(5 ⋅ (4 p + 1))\)
\(\text{ } = {}^{2}\!\log(20 p + 5)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(2 ⋅ {}^{5}\!\log(a + 3)\)

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

c

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

1p

○

\(\text{ } = {}^{5}\!\log(a^{2} + 6 a + 9)\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(5 + {}^{3}\!\log(4 x + 2)\)
\(\text{ } = {}^{3}\!\log(3^{5}) + {}^{3}\!\log(4 x + 2)\)
\(\text{ } = {}^{3}\!\log(243) + {}^{3}\!\log(4 x + 2)\)

1p

○

\(\text{ } = {}^{3}\!\log(243 ⋅ (4 x + 2))\)
\(\text{ } = {}^{3}\!\log(972 x + 486)\)

1p

3p

b

\({}^{5}\!\log(625) + {}^{2}\!\log(3 x + 1)\)

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

b

\({}^{5}\!\log(625) + {}^{2}\!\log(3 x + 1)\)
\(\text{ } = {}^{5}\!\log(5^{4}) + {}^{2}\!\log(3 x + 1)\)
\(\text{ } = 4 + {}^{2}\!\log(3 x + 1)\)

1p

○

\(\text{ } = {}^{2}\!\log(2^{4}) + {}^{2}\!\log(3 x + 1)\)
\(\text{ } = {}^{2}\!\log(16) + {}^{2}\!\log(3 x + 1)\)

1p

○

\(\text{ } = {}^{2}\!\log(16 ⋅ (3 x + 1))\)
\(\text{ } = {}^{2}\!\log(48 x + 16)\)

1p

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