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

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

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

a

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

1p

1p

b

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

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

b

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

1p

2p

c

\(5⋅{}^{3}\!\log(4a)\)

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

c

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

1p

○

\(\text{ }={}^{3}\!\log(1\,024a^5)\)

1p

2p

d

\(2⋅{}^{5}\!\log(x)+{}^{5}\!\log(4x+1)\)

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(3+{}^{4}\!\log(p-5)\)
\(\text{ }={}^{4}\!\log(4^3)+{}^{4}\!\log(p-5)\)
\(\text{ }={}^{4}\!\log(64)+{}^{4}\!\log(p-5)\)

1p

○

\(\text{ }={}^{4}\!\log(64⋅(p-5))\)
\(\text{ }={}^{4}\!\log(64p-320)\)

1p

3p

b

\({}^{5}\!\log(125)+{}^{4}\!\log(2x+1)\)

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

b

\({}^{5}\!\log(125)+{}^{4}\!\log(2x+1)\)
\(\text{ }={}^{5}\!\log(5^3)+{}^{4}\!\log(2x+1)\)
\(\text{ }=3+{}^{4}\!\log(2x+1)\)

1p

○

\(\text{ }={}^{4}\!\log(4^3)+{}^{4}\!\log(2x+1)\)
\(\text{ }={}^{4}\!\log(64)+{}^{4}\!\log(2x+1)\)

1p

○

\(\text{ }={}^{4}\!\log(64⋅(2x+1))\)
\(\text{ }={}^{4}\!\log(128x+64)\)

1p
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