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

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

Optellen (1)
00ku - Logaritmen herleiden - basis - basis - 2ms - dynamic variables

a

\({}^{5}\!\log(2a)+{}^{5}\!\log(3a-1)\)
\(\text{ }={}^{5}\!\log(2a⋅(3a-1))\)
\(\text{ }={}^{5}\!\log(6a^2-2a)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(3⋅{}^{4}\!\log(2p)\)

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

c

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

1p

○

\(\text{ }={}^{4}\!\log(8p^3)\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(2+{}^{5}\!\log(3x-1)\)
\(\text{ }={}^{5}\!\log(5^2)+{}^{5}\!\log(3x-1)\)
\(\text{ }={}^{5}\!\log(25)+{}^{5}\!\log(3x-1)\)

1p

○

\(\text{ }={}^{5}\!\log(25⋅(3x-1))\)
\(\text{ }={}^{5}\!\log(75x-25)\)

1p

3p

b

\({}^{2}\!\log(16)+{}^{3}\!\log(x-5)\)

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

b

\({}^{2}\!\log(16)+{}^{3}\!\log(x-5)\)
\(\text{ }={}^{2}\!\log(2^4)+{}^{3}\!\log(x-5)\)
\(\text{ }=4+{}^{3}\!\log(x-5)\)

1p

○

\(\text{ }={}^{3}\!\log(3^4)+{}^{3}\!\log(x-5)\)
\(\text{ }={}^{3}\!\log(81)+{}^{3}\!\log(x-5)\)

1p

○

\(\text{ }={}^{3}\!\log(81⋅(x-5))\)
\(\text{ }={}^{3}\!\log(81x-405)\)

1p
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