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

\({}^{5}\!\log(4) + {}^{5}\!\log(3 p - 1)\)

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

a

\({}^{5}\!\log(4) + {}^{5}\!\log(3 p - 1)\)
\(\text{ } = {}^{5}\!\log(4 ⋅ (3 p - 1))\)
\(\text{ } = {}^{5}\!\log(12 p - 4)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(5 ⋅ {}^{3}\!\log(2 x)\)

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

c

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

1p

\(\text{ } = {}^{3}\!\log(32 x^{5})\)

1p

2p

d

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

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

d

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

1p

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(3 + {}^{4}\!\log(2 a - 1)\)
\(\text{ } = {}^{4}\!\log(4^{3}) + {}^{4}\!\log(2 a - 1)\)
\(\text{ } = {}^{4}\!\log(64) + {}^{4}\!\log(2 a - 1)\)

1p

\(\text{ } = {}^{4}\!\log(64 ⋅ (2 a - 1))\)
\(\text{ } = {}^{4}\!\log(128 a - 64)\)

1p

3p

b

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

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

b

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

1p

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

1p

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

1p

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