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

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

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

a

\({}^{4}\!\log(3)+{}^{4}\!\log(2a+5)\)
\(\text{ }={}^{4}\!\log(3⋅(2a+5))\)
\(\text{ }={}^{4}\!\log(6a+15)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(5⋅{}^{3}\!\log(4x)\)

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

c

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

1p

○

\(\text{ }={}^{3}\!\log(1\,024x^5)\)

1p

2p

d

\(4⋅{}^{3}\!\log(p)+{}^{3}\!\log(2p-1)\)

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(5+{}^{2}\!\log(x-4)\)
\(\text{ }={}^{2}\!\log(2^5)+{}^{2}\!\log(x-4)\)
\(\text{ }={}^{2}\!\log(32)+{}^{2}\!\log(x-4)\)

1p

○

\(\text{ }={}^{2}\!\log(32⋅(x-4))\)
\(\text{ }={}^{2}\!\log(32x-128)\)

1p

3p

b

\({}^{5}\!\log(125)+{}^{4}\!\log(x+2)\)

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

b

\({}^{5}\!\log(125)+{}^{4}\!\log(x+2)\)
\(\text{ }={}^{5}\!\log(5^3)+{}^{4}\!\log(x+2)\)
\(\text{ }=3+{}^{4}\!\log(x+2)\)

1p

○

\(\text{ }={}^{4}\!\log(4^3)+{}^{4}\!\log(x+2)\)
\(\text{ }={}^{4}\!\log(64)+{}^{4}\!\log(x+2)\)

1p

○

\(\text{ }={}^{4}\!\log(64⋅(x+2))\)
\(\text{ }={}^{4}\!\log(64x+128)\)

1p
"