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

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

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

a

\({}^{2}\!\log(4)+{}^{2}\!\log(3a-5)\)
\(\text{ }={}^{2}\!\log(4⋅(3a-5))\)
\(\text{ }={}^{2}\!\log(12a-20)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(5⋅{}^{3}\!\log(4x)\)

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

c

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

1p

○

\(\text{ }={}^{3}\!\log(1\,024x^5)\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

○

\(\text{ }={}^{4}\!\log(64⋅(5a+2))\)
\(\text{ }={}^{4}\!\log(320a+128)\)

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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