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

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

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

a

\({}^{3}\!\log(4p)+{}^{3}\!\log(2p+1)\)
\(\text{ }={}^{3}\!\log(4p⋅(2p+1))\)
\(\text{ }={}^{3}\!\log(8p^2+4p)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(5⋅{}^{4}\!\log(3x)\)

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

c

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

1p

○

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

1p

2p

d

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

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

d

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

1p

○

\(\text{ }={}^{2}\!\log(a^5⋅(4a-3))\)
\(\text{ }={}^{2}\!\log(4a^6-3a^5)\)

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(3+{}^{2}\!\log(5a+1)\)
\(\text{ }={}^{2}\!\log(2^3)+{}^{2}\!\log(5a+1)\)
\(\text{ }={}^{2}\!\log(8)+{}^{2}\!\log(5a+1)\)

1p

○

\(\text{ }={}^{2}\!\log(8⋅(5a+1))\)
\(\text{ }={}^{2}\!\log(40a+8)\)

1p

3p

b

\({}^{4}\!\log(64)+{}^{5}\!\log(2x+1)\)

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

b

\({}^{4}\!\log(64)+{}^{5}\!\log(2x+1)\)
\(\text{ }={}^{4}\!\log(4^3)+{}^{5}\!\log(2x+1)\)
\(\text{ }=3+{}^{5}\!\log(2x+1)\)

1p

○

\(\text{ }={}^{5}\!\log(5^3)+{}^{5}\!\log(2x+1)\)
\(\text{ }={}^{5}\!\log(125)+{}^{5}\!\log(2x+1)\)

1p

○

\(\text{ }={}^{5}\!\log(125⋅(2x+1))\)
\(\text{ }={}^{5}\!\log(250x+125)\)

1p
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