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

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

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

a

\({}^{2}\!\log(5)+{}^{2}\!\log(4a-3)\)
\(\text{ }={}^{2}\!\log(5⋅(4a-3))\)
\(\text{ }={}^{2}\!\log(20a-15)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(3⋅{}^{5}\!\log(4a)\)

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

c

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

1p

○

\(\text{ }={}^{5}\!\log(64a^3)\)

1p

2p

d

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

OptellenVermenigvuldigen
00kx - Logaritmen herleiden - basis - eind - 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

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

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

a

\(5+{}^{3}\!\log(p-2)\)
\(\text{ }={}^{3}\!\log(3^5)+{}^{3}\!\log(p-2)\)
\(\text{ }={}^{3}\!\log(243)+{}^{3}\!\log(p-2)\)

1p

○

\(\text{ }={}^{3}\!\log(243⋅(p-2))\)
\(\text{ }={}^{3}\!\log(243p-486)\)

1p

3p

b

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

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

b

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

1p

○

\(\text{ }={}^{4}\!\log(4^5)+{}^{4}\!\log(a+2)\)
\(\text{ }={}^{4}\!\log(1\,024)+{}^{4}\!\log(a+2)\)

1p

○

\(\text{ }={}^{4}\!\log(1\,024⋅(a+2))\)
\(\text{ }={}^{4}\!\log(1\,024a+2\,048)\)

1p
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