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

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

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

a

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

1p

1p

b

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

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

b

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

1p

2p

c

\(2⋅{}^{5}\!\log(4p)\)

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

c

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

1p

○

\(\text{ }={}^{5}\!\log(16p^2)\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

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

1p

○

\(\text{ }={}^{2}\!\log(32⋅(x-3))\)
\(\text{ }={}^{2}\!\log(32x-96)\)

1p

3p

b

\({}^{5}\!\log(25)+{}^{4}\!\log(a-3)\)

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

b

\({}^{5}\!\log(25)+{}^{4}\!\log(a-3)\)
\(\text{ }={}^{5}\!\log(5^2)+{}^{4}\!\log(a-3)\)
\(\text{ }=2+{}^{4}\!\log(a-3)\)

1p

○

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

1p

○

\(\text{ }={}^{4}\!\log(16⋅(a-3))\)
\(\text{ }={}^{4}\!\log(16a-48)\)

1p
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