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

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

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

a

\({}^{3}\!\log(4 a) + {}^{3}\!\log(5 a - 2)\)
\(\text{ } = {}^{3}\!\log(4 a ⋅ (5 a - 2))\)
\(\text{ } = {}^{3}\!\log(20 a^{2} - 8 a)\)

1p

1p

b

\({}^{2}\!\log(5) - {}^{2}\!\log(3 p - 1)\)

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

b

\({}^{2}\!\log(5) - {}^{2}\!\log(3 p - 1)\)
\(\text{ } = {}^{2}\!\log({5 \over 3 p - 1})\)

1p

2p

c

\(4 ⋅ {}^{2}\!\log(3 x)\)

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

c

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

1p

\(\text{ } = {}^{2}\!\log(81 x^{4})\)

1p

2p

d

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

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

d

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

1p

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

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

1p

3p

b

\({}^{4}\!\log(64) + {}^{5}\!\log(x - 2)\)

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

b

\({}^{4}\!\log(64) + {}^{5}\!\log(x - 2)\)
\(\text{ } = {}^{4}\!\log(4^{3}) + {}^{5}\!\log(x - 2)\)
\(\text{ } = 3 + {}^{5}\!\log(x - 2)\)

1p

\(\text{ } = {}^{5}\!\log(5^{3}) + {}^{5}\!\log(x - 2)\)
\(\text{ } = {}^{5}\!\log(125) + {}^{5}\!\log(x - 2)\)

1p

\(\text{ } = {}^{5}\!\log(125 ⋅ (x - 2))\)
\(\text{ } = {}^{5}\!\log(125 x - 250)\)

1p

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