Getal & Ruimte (12e editie) - vwo wiskunde B

'Logaritmen herleiden'.

vwo wiskunde B 9.1 Rekenregels voor logaritmen

Logaritmen herleiden (6)

opgave 1

Herleid tot één logaritme.

1p

a

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

Optellen (1)
00ku - Logaritmen herleiden - basis - basis - 2ms - dynamic variables

a

\({}^{5}\!\log(3)+{}^{5}\!\log(2x+4)\)
\(\text{ }={}^{5}\!\log(3⋅(2x+4))\)
\(\text{ }={}^{5}\!\log(6x+12)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(3⋅{}^{5}\!\log(4x)\)

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

c

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

1p

○

\(\text{ }={}^{5}\!\log(64x^3)\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

○

\(\text{ }={}^{5}\!\log(625⋅(3p+2))\)
\(\text{ }={}^{5}\!\log(1\,875p+1\,250)\)

1p

3p

b

\({}^{3}\!\log(9)+{}^{4}\!\log(a-5)\)

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

b

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

1p

○

\(\text{ }={}^{4}\!\log(4^2)+{}^{4}\!\log(a-5)\)
\(\text{ }={}^{4}\!\log(16)+{}^{4}\!\log(a-5)\)

1p

○

\(\text{ }={}^{4}\!\log(16⋅(a-5))\)
\(\text{ }={}^{4}\!\log(16a-80)\)

1p
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