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

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

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

a

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

1p

1p

b

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

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

b

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

1p

2p

c

\(2⋅{}^{3}\!\log(5a)\)

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

c

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

1p

○

\(\text{ }={}^{3}\!\log(25a^2)\)

1p

2p

d

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

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

d

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

1p

○

\(\text{ }={}^{3}\!\log(p^2⋅(5p-1))\)
\(\text{ }={}^{3}\!\log(5p^3-p^2)\)

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(4+{}^{3}\!\log(5a-1)\)
\(\text{ }={}^{3}\!\log(3^4)+{}^{3}\!\log(5a-1)\)
\(\text{ }={}^{3}\!\log(81)+{}^{3}\!\log(5a-1)\)

1p

○

\(\text{ }={}^{3}\!\log(81⋅(5a-1))\)
\(\text{ }={}^{3}\!\log(405a-81)\)

1p

3p

b

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

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

b

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

1p

○

\(\text{ }={}^{5}\!\log(5^2)+{}^{5}\!\log(3a-1)\)
\(\text{ }={}^{5}\!\log(25)+{}^{5}\!\log(3a-1)\)

1p

○

\(\text{ }={}^{5}\!\log(25⋅(3a-1))\)
\(\text{ }={}^{5}\!\log(75a-25)\)

1p
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