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

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

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

a

\({}^{3}\!\log(5x)+{}^{3}\!\log(4x+2)\)
\(\text{ }={}^{3}\!\log(5x⋅(4x+2))\)
\(\text{ }={}^{3}\!\log(20x^2+10x)\)

1p

1p

b

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

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

b

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

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

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

\(5+{}^{4}\!\log(3a+1)\)

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

a

\(5+{}^{4}\!\log(3a+1)\)
\(\text{ }={}^{4}\!\log(4^5)+{}^{4}\!\log(3a+1)\)
\(\text{ }={}^{4}\!\log(1\,024)+{}^{4}\!\log(3a+1)\)

1p

○

\(\text{ }={}^{4}\!\log(1\,024⋅(3a+1))\)
\(\text{ }={}^{4}\!\log(3\,072a+1\,024)\)

1p

3p

b

\({}^{4}\!\log(16)+{}^{3}\!\log(5p+1)\)

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

b

\({}^{4}\!\log(16)+{}^{3}\!\log(5p+1)\)
\(\text{ }={}^{4}\!\log(4^2)+{}^{3}\!\log(5p+1)\)
\(\text{ }=2+{}^{3}\!\log(5p+1)\)

1p

○

\(\text{ }={}^{3}\!\log(3^2)+{}^{3}\!\log(5p+1)\)
\(\text{ }={}^{3}\!\log(9)+{}^{3}\!\log(5p+1)\)

1p

○

\(\text{ }={}^{3}\!\log(9⋅(5p+1))\)
\(\text{ }={}^{3}\!\log(45p+9)\)

1p
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