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

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

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

a

\({}^{2}\!\log(3)+{}^{2}\!\log(a-5)\)
\(\text{ }={}^{2}\!\log(3⋅(a-5))\)
\(\text{ }={}^{2}\!\log(3a-15)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(2⋅{}^{5}\!\log(x+1)\)

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

c

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

1p

○

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

1p

2p

d

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

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

d

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

1p

○

\(\text{ }={}^{5}\!\log(a^2⋅(4a-1))\)
\(\text{ }={}^{5}\!\log(4a^3-a^2)\)

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

○

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

1p

3p

b

\({}^{2}\!\log(32)+{}^{4}\!\log(3p+1)\)

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

b

\({}^{2}\!\log(32)+{}^{4}\!\log(3p+1)\)
\(\text{ }={}^{2}\!\log(2^5)+{}^{4}\!\log(3p+1)\)
\(\text{ }=5+{}^{4}\!\log(3p+1)\)

1p

○

\(\text{ }={}^{4}\!\log(4^5)+{}^{4}\!\log(3p+1)\)
\(\text{ }={}^{4}\!\log(1\,024)+{}^{4}\!\log(3p+1)\)

1p

○

\(\text{ }={}^{4}\!\log(1\,024⋅(3p+1))\)
\(\text{ }={}^{4}\!\log(3\,072p+1\,024)\)

1p
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