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

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

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

a

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

1p

1p

b

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

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

b

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

1p

2p

c

\(3⋅{}^{4}\!\log(5a)\)

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

c

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

1p

○

\(\text{ }={}^{4}\!\log(125a^3)\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(2+{}^{4}\!\log(3x+5)\)
\(\text{ }={}^{4}\!\log(4^2)+{}^{4}\!\log(3x+5)\)
\(\text{ }={}^{4}\!\log(16)+{}^{4}\!\log(3x+5)\)

1p

○

\(\text{ }={}^{4}\!\log(16⋅(3x+5))\)
\(\text{ }={}^{4}\!\log(48x+80)\)

1p

3p

b

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

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

b

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

1p

○

\(\text{ }={}^{3}\!\log(3^4)+{}^{3}\!\log(a+2)\)
\(\text{ }={}^{3}\!\log(81)+{}^{3}\!\log(a+2)\)

1p

○

\(\text{ }={}^{3}\!\log(81⋅(a+2))\)
\(\text{ }={}^{3}\!\log(81a+162)\)

1p
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