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

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

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

a

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

1p

1p

b

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

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

b

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

1p

2p

c

\(4⋅{}^{3}\!\log(2x)\)

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

c

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

1p

○

\(\text{ }={}^{3}\!\log(16x^4)\)

1p

2p

d

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

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

d

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

1p

○

\(\text{ }={}^{2}\!\log(a^5⋅(4a+1))\)
\(\text{ }={}^{2}\!\log(4a^6+a^5)\)

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(4+{}^{5}\!\log(p-3)\)
\(\text{ }={}^{5}\!\log(5^4)+{}^{5}\!\log(p-3)\)
\(\text{ }={}^{5}\!\log(625)+{}^{5}\!\log(p-3)\)

1p

○

\(\text{ }={}^{5}\!\log(625⋅(p-3))\)
\(\text{ }={}^{5}\!\log(625p-1\,875)\)

1p

3p

b

\({}^{5}\!\log(625)+{}^{2}\!\log(p-3)\)

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

b

\({}^{5}\!\log(625)+{}^{2}\!\log(p-3)\)
\(\text{ }={}^{5}\!\log(5^4)+{}^{2}\!\log(p-3)\)
\(\text{ }=4+{}^{2}\!\log(p-3)\)

1p

○

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

1p

○

\(\text{ }={}^{2}\!\log(16⋅(p-3))\)
\(\text{ }={}^{2}\!\log(16p-48)\)

1p
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