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

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

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

a

\({}^{4}\!\log(3x)+{}^{4}\!\log(5x+1)\)
\(\text{ }={}^{4}\!\log(3x⋅(5x+1))\)
\(\text{ }={}^{4}\!\log(15x^2+3x)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(5⋅{}^{2}\!\log(4a)\)

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

c

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

1p

○

\(\text{ }={}^{2}\!\log(1\,024a^5)\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(3+{}^{2}\!\log(4p-5)\)
\(\text{ }={}^{2}\!\log(2^3)+{}^{2}\!\log(4p-5)\)
\(\text{ }={}^{2}\!\log(8)+{}^{2}\!\log(4p-5)\)

1p

○

\(\text{ }={}^{2}\!\log(8⋅(4p-5))\)
\(\text{ }={}^{2}\!\log(32p-40)\)

1p

3p

b

\({}^{5}\!\log(625)+{}^{2}\!\log(3x+1)\)

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

b

\({}^{5}\!\log(625)+{}^{2}\!\log(3x+1)\)
\(\text{ }={}^{5}\!\log(5^4)+{}^{2}\!\log(3x+1)\)
\(\text{ }=4+{}^{2}\!\log(3x+1)\)

1p

○

\(\text{ }={}^{2}\!\log(2^4)+{}^{2}\!\log(3x+1)\)
\(\text{ }={}^{2}\!\log(16)+{}^{2}\!\log(3x+1)\)

1p

○

\(\text{ }={}^{2}\!\log(16⋅(3x+1))\)
\(\text{ }={}^{2}\!\log(48x+16)\)

1p
"