Getal & Ruimte (12e editie) - vwo wiskunde B

'Logaritmen herleiden'.

vwo wiskunde B 9.1 Rekenregels voor logaritmen

Logaritmen herleiden (6)

opgave 1

Herleid tot één logaritme.

1p

a

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

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

a

\({}^{3}\!\log(5x)+{}^{3}\!\log(2x-1)\)
\(\text{ }={}^{3}\!\log(5x⋅(2x-1))\)
\(\text{ }={}^{3}\!\log(10x^2-5x)\)

1p

1p

b

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

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

b

\({}^{2}\!\log(4)-{}^{2}\!\log(5x-1)\)
\(\text{ }={}^{2}\!\log({4 \over 5x-1})\)

1p

2p

c

\(4⋅{}^{2}\!\log(5a)\)

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

c

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

1p

○

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

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(5+{}^{3}\!\log(2a+4)\)
\(\text{ }={}^{3}\!\log(3^5)+{}^{3}\!\log(2a+4)\)
\(\text{ }={}^{3}\!\log(243)+{}^{3}\!\log(2a+4)\)

1p

○

\(\text{ }={}^{3}\!\log(243⋅(2a+4))\)
\(\text{ }={}^{3}\!\log(486a+972)\)

1p

3p

b

\({}^{2}\!\log(32)+{}^{3}\!\log(4p-1)\)

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

b

\({}^{2}\!\log(32)+{}^{3}\!\log(4p-1)\)
\(\text{ }={}^{2}\!\log(2^5)+{}^{3}\!\log(4p-1)\)
\(\text{ }=5+{}^{3}\!\log(4p-1)\)

1p

○

\(\text{ }={}^{3}\!\log(3^5)+{}^{3}\!\log(4p-1)\)
\(\text{ }={}^{3}\!\log(243)+{}^{3}\!\log(4p-1)\)

1p

○

\(\text{ }={}^{3}\!\log(243⋅(4p-1))\)
\(\text{ }={}^{3}\!\log(972p-243)\)

1p
"