Getal & Ruimte (12e editie) - havo wiskunde B

'Logaritmen herleiden'.

havo wiskunde B 9.3 Rekenregels voor logaritmen

Logaritmen herleiden (6)

opgave 1

Herleid tot één logaritme.

1p

a

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

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

a

\({}^{5}\!\log(2)+{}^{5}\!\log(4a-1)\)
\(\text{ }={}^{5}\!\log(2⋅(4a-1))\)
\(\text{ }={}^{5}\!\log(8a-2)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(5⋅{}^{2}\!\log(4x)\)

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

c

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

1p

○

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

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(2+{}^{3}\!\log(x-5)\)
\(\text{ }={}^{3}\!\log(3^2)+{}^{3}\!\log(x-5)\)
\(\text{ }={}^{3}\!\log(9)+{}^{3}\!\log(x-5)\)

1p

○

\(\text{ }={}^{3}\!\log(9⋅(x-5))\)
\(\text{ }={}^{3}\!\log(9x-45)\)

1p

3p

b

\({}^{2}\!\log(32)+{}^{3}\!\log(a-4)\)

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

b

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

1p

○

\(\text{ }={}^{3}\!\log(3^5)+{}^{3}\!\log(a-4)\)
\(\text{ }={}^{3}\!\log(243)+{}^{3}\!\log(a-4)\)

1p

○

\(\text{ }={}^{3}\!\log(243⋅(a-4))\)
\(\text{ }={}^{3}\!\log(243a-972)\)

1p
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