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

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

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

b

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

1p

2p

c

\(3⋅{}^{2}\!\log(5x)\)

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

c

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

1p

○

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

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

○

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

1p

3p

b

\({}^{3}\!\log(243)+{}^{2}\!\log(x+4)\)

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

b

\({}^{3}\!\log(243)+{}^{2}\!\log(x+4)\)
\(\text{ }={}^{3}\!\log(3^5)+{}^{2}\!\log(x+4)\)
\(\text{ }=5+{}^{2}\!\log(x+4)\)

1p

○

\(\text{ }={}^{2}\!\log(2^5)+{}^{2}\!\log(x+4)\)
\(\text{ }={}^{2}\!\log(32)+{}^{2}\!\log(x+4)\)

1p

○

\(\text{ }={}^{2}\!\log(32⋅(x+4))\)
\(\text{ }={}^{2}\!\log(32x+128)\)

1p
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