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

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

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

a

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

1p

1p

b

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

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

b

\({}^{2}\!\log(5 x) - {}^{2}\!\log(x - 4)\)
\(\text{ } = {}^{2}\!\log({5 x \over x - 4})\)

1p

2p

c

\(2 ⋅ {}^{4}\!\log(5 x)\)

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

c

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

1p

\(\text{ } = {}^{4}\!\log(25 x^{2})\)

1p

2p

d

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

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

d

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

1p

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

\(\text{ } = {}^{3}\!\log(81 ⋅ (2 a - 5))\)
\(\text{ } = {}^{3}\!\log(162 a - 405)\)

1p

3p

b

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

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

b

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

1p

\(\text{ } = {}^{4}\!\log(4^{2}) + {}^{4}\!\log(5 p + 1)\)
\(\text{ } = {}^{4}\!\log(16) + {}^{4}\!\log(5 p + 1)\)

1p

\(\text{ } = {}^{4}\!\log(16 ⋅ (5 p + 1))\)
\(\text{ } = {}^{4}\!\log(80 p + 16)\)

1p

"