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

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

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

a

\({}^{3}\!\log(4)+{}^{3}\!\log(5x-1)\)
\(\text{ }={}^{3}\!\log(4⋅(5x-1))\)
\(\text{ }={}^{3}\!\log(20x-4)\)

1p

1p

b

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

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

b

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

1p

2p

c

\(3⋅{}^{2}\!\log(5p)\)

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

c

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

1p

○

\(\text{ }={}^{2}\!\log(125p^3)\)

1p

2p

d

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

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

d

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

1p

○

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

1p

opgave 2

Herleid tot één logaritme.

2p

a

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

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

a

\(2+{}^{5}\!\log(3a+4)\)
\(\text{ }={}^{5}\!\log(5^2)+{}^{5}\!\log(3a+4)\)
\(\text{ }={}^{5}\!\log(25)+{}^{5}\!\log(3a+4)\)

1p

○

\(\text{ }={}^{5}\!\log(25⋅(3a+4))\)
\(\text{ }={}^{5}\!\log(75a+100)\)

1p

3p

b

\({}^{5}\!\log(625)+{}^{2}\!\log(p-3)\)

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

b

\({}^{5}\!\log(625)+{}^{2}\!\log(p-3)\)
\(\text{ }={}^{5}\!\log(5^4)+{}^{2}\!\log(p-3)\)
\(\text{ }=4+{}^{2}\!\log(p-3)\)

1p

○

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

1p

○

\(\text{ }={}^{2}\!\log(16⋅(p-3))\)
\(\text{ }={}^{2}\!\log(16p-48)\)

1p
"