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

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

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

a

\({}^{5}\!\log(2)+{}^{5}\!\log(4a+3)\)
\(\text{ }={}^{5}\!\log(2⋅(4a+3))\)
\(\text{ }={}^{5}\!\log(8a+6)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(3⋅{}^{5}\!\log(2p)\)

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

c

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

1p

○

\(\text{ }={}^{5}\!\log(8p^3)\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(4+{}^{5}\!\log(2a+1)\)
\(\text{ }={}^{5}\!\log(5^4)+{}^{5}\!\log(2a+1)\)
\(\text{ }={}^{5}\!\log(625)+{}^{5}\!\log(2a+1)\)

1p

○

\(\text{ }={}^{5}\!\log(625⋅(2a+1))\)
\(\text{ }={}^{5}\!\log(1\,250a+625)\)

1p

3p

b

\({}^{4}\!\log(64)+{}^{2}\!\log(5x+1)\)

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

b

\({}^{4}\!\log(64)+{}^{2}\!\log(5x+1)\)
\(\text{ }={}^{4}\!\log(4^3)+{}^{2}\!\log(5x+1)\)
\(\text{ }=3+{}^{2}\!\log(5x+1)\)

1p

○

\(\text{ }={}^{2}\!\log(2^3)+{}^{2}\!\log(5x+1)\)
\(\text{ }={}^{2}\!\log(8)+{}^{2}\!\log(5x+1)\)

1p

○

\(\text{ }={}^{2}\!\log(8⋅(5x+1))\)
\(\text{ }={}^{2}\!\log(40x+8)\)

1p
"