Logaritmische formules herleiden

0w - 11 oefeningen

Dubbel (1)
00ks - Logaritmische formules herleiden - basis - 0ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.4

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(y = 770 x^{-1{,}68}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\)
Geef \(a\) in twee decimalen.

\(y = 770 x^{-1{,}68}\)
\(\log(y) = \log(770 x^{-1{,}68})\)

1p

\(\log(y) = \log(770) + \log(x^{-1{,}68})\)
\(\log(y) = \log(770) - 1{,}68 ⋅ \log(x)\)

1p

\(\log(y) = 2{,}886... - 1{,}68 ⋅ \log(x)\)
Dus \(y = 2{,}89 - 1{,}68 ⋅ \log(x) \text{.}\)

1p

Dubbel (2)
00kt - Logaritmische formules herleiden - basis - 0ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.4

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(y = {450 \over x^{2} \sqrt{x}}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\)
Geef \(a\) in twee decimalen.

\(y = {450 \over x^{2} \sqrt{x}} = 450 x^{-2{,}5}\)
\(\log(y) = \log(450 x^{-2{,}5})\)

1p

\(\log(y) = \log(450) + \log(x^{-2{,}5})\)
\(\log(y) = \log(450) - 2{,}5 ⋅ \log(x)\)

1p

\(\log(y) = 2{,}653... - 2{,}5 ⋅ \log(x)\)
Dus \(y = 2{,}65 - 2{,}5 ⋅ \log(x) \text{.}\)

1p

Dubbel (3)
00kr - Logaritmische formules herleiden - basis - 0ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.4

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(\log(y) = 3{,}12 - 1{,}12 ⋅ \log(x)\) in de vorm \(y = a x^{b} \text{.}\)
Geef \(a\) in gehelen.

\(\log(y) = 3{,}12 - 1{,}12 ⋅ \log(x)\)
\(\log(y) = \log(10^{3{,}12}) + \log(x^{-1{,}12})\)
\(\log(y) = \log(10^{3{,}12} ⋅ x^{-1{,}12})\)

1p

\(y = 10^{3{,}12} ⋅ x^{-1{,}12}\)

1p

\(y = 1318{,}256... ⋅ x^{-1{,}12}\)
Dus \(y = 1\,318 ⋅ x^{-1{,}12} \text{.}\)

1p

Herleiden (1)
00ko - Logaritmische formules herleiden - basis - 0ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.4 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(y = 4\,400 ⋅ 0{,}74^{x}\) in de vorm \(\log(y) = a x + b \text{.}\)
Geef \(a\) in vier decimalen en \(b\) in twee decimalen.

\(y = 4\,400 ⋅ 0{,}74^{x}\)
\(\log(y) = \log(4\,400 ⋅ 0{,}74^{x})\)
\(\log(y) = \log(4\,400) + \log(0{,}74^{x})\)

1p

\(\log(y) = \log(4\,400) + x ⋅ \log(0{,}74)\)

1p

\(\log(y) = 3{,}643... + x ⋅ -0{,}13076...\)
Dus \(\log(y) = -0{,}1308 x + 3{,}64\)

1p

Herleiden (2)
00kp - Logaritmische formules herleiden - basis - 1ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.4 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(y = 7\,500 ⋅ 0{,}83^{5 x + 3}\) in de vorm \(\log(y) = a x + b \text{.}\)
Geef \(a\) in vier decimalen en \(b\) in twee decimalen.

\(y = 7\,500 ⋅ 0{,}83^{5 x + 3}\)
\(\log(y) = \log(7\,500 ⋅ 0{,}83^{5 x + 3})\)
\(\log(y) = \log(7\,500) + \log(0{,}83^{5 x + 3})\)

1p

\(\log(y) = \log(7\,500) + (5 x + 3) ⋅ \log(0{,}83)\)
\(\log(y) = \log(7\,500) + 5 x ⋅ \log(0{,}83) + 3 ⋅ \log(0{,}83)\)

1p

\(\log(y) = 3{,}875... + 5 x ⋅ -0{,}08092... + 3 ⋅ -0{,}08092...\)
\(\log(y) = 3{,}875... - 0{,}40460... ⋅ x - 0{,}24276...\)
Dus \(\log(y) = -0{,}4046 x + 3{,}63\)

1p

Herleiden (3)
00kq - Logaritmische formules herleiden - basis - 0ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.4 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(\log(y) = -0{,}9398 x + 2{,}41\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Geef \(b\) in gehelen en \(g\) in twee decimalen.

\(\log(y) = -0{,}9398 x + 2{,}41\)
\(y = 10^{-0{,}9398 x + 2{,}41}\)

1p

\(y = 10^{-0{,}9398 x} ⋅ 10^{2{,}41}\)
\(y = (10^{-0{,}9398})^{x} ⋅ 10^{2{,}41}\)

1p

\(y = 0{,}114...^{x} ⋅ 257{,}039...\)
Dus \(y = 257 ⋅ 0{,}11^{x} \text{.}\)

1p

Herleiden (4)
00l0 - Logaritmische formules herleiden - basis - 0ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.3

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(y = 1{,}37 ⋅ {}^{5}\!\log(x) - 2{,}36\) in de vorm \(y = {}^{5}\!\log(a x^{b}) \text{.}\)
Geef \(a\) en \(b\) in twee decimalen.

\(y = 1{,}37 ⋅ {}^{5}\!\log(x) - 2{,}36\)
\(\text{ } = {}^{5}\!\log(x^{1{,}37}) - 2{,}36\)

1p

\(\text{ } = {}^{5}\!\log(x^{1{,}37}) + {}^{5}\!\log(5^{-2{,}36})\)
\(\text{ } = {}^{5}\!\log(x^{1{,}37} ⋅ 5^{-2{,}36})\)

1p

\(\text{ } = {}^{5}\!\log(x^{1{,}37} ⋅ 0{,}022...)\)
Dus \(y = {}^{5}\!\log(0{,}02 ⋅ x^{1{,}37}) \text{.}\)

1p

Herleiden (6)
00l2 - Logaritmische formules herleiden - basis - 0ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.3 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(y = {}^{4}\!\log(1{,}6 x) + 1{,}2\) in de vorm \(y = a + b ⋅ {}^{5}\!\log(x) \text{.}\)
Geef \(a\) en \(b\) in twee decimalen.

\(y = {}^{4}\!\log(1{,}6 x) + 1{,}2\)
\(\text{ } = {}^{4}\!\log(1{,}6) + {}^{4}\!\log(x) + 1{,}2\)

1p

\(\text{ } = {}^{4}\!\log(1{,}6) + 1{,}2 + {{}^{5}\!\log(x) \over {}^{5}\!\log(4)}\)
\(\text{ } = {}^{4}\!\log(1{,}6) + 1{,}2 + {1 \over {}^{5}\!\log(4)} ⋅ {}^{5}\!\log(x)\)

1p

\(\text{ } = 0{,}339... + 1{,}2 + {1 \over 0{,}861...} ⋅ {}^{5}\!\log(x)\)
\(\text{ } = 1{,}539... + 1{,}160... ⋅ {}^{5}\!\log(x)\)
Dus \(y = 1{,}54 + 1{,}16 ⋅ {}^{5}\!\log(x) \text{.}\)

1p

Herleiden (7)
00l3 - Logaritmische formules herleiden - basis - 1ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.3

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(y = 9 ⋅ \log(2\,000 x) - 5\) in de vorm \(y = a + b ⋅ \log(2 x) \text{.}\)

\(y = 9 ⋅ \log(2\,000 x) - 5\)
\(\text{ } = 9 ⋅ (\log(1\,000) + \log(2 x)) - 5\)

1p

\(\text{ } = 9 ⋅ (3 + \log(2 x)) - 5\)

1p

\(\text{ } = 27 + 9 ⋅ \log(2 x) - 5\)
\(\text{ } = 22 + 9 ⋅ \log(2 x)\)

1p

Logaritmisch (5)
00l1 - Logaritmische formules herleiden - basis - 0ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.3

Herleid tot de gevraagde vorm.

3p

Schrijf de formule \(y = {}^{3}\!\log(71 x^{5})\) in de vorm \(y = a + b ⋅ {}^{3}\!\log(x) \text{.}\)
Geef \(a\) in twee decimalen.

\(y = {}^{3}\!\log(71 x^{5})\)
\(\text{ } = {}^{3}\!\log(71 x^{5})\)

1p

\(\text{ } = {}^{3}\!\log(71) + {}^{3}\!\log(x^{5})\)
\(\text{ } = {}^{3}\!\log(71) + 5 ⋅ {}^{3}\!\log(x)\)

1p

\(\text{ } = 3{,}880... + 5 ⋅ {}^{3}\!\log(x)\)
Dus \(y = 3{,}88 + 5 ⋅ {}^{3}\!\log(x) \text{.}\)

1p

Vrijmaken
00kn - Logaritmische formules herleiden - basis - 1ms - dynamic variables
Getal & Ruimte (12e editie) - havo wiskunde B - 9.2 Getal & Ruimte (12e editie) - vwo wiskunde A - 13.4 Getal & Ruimte (12e editie) - vwo wiskunde B - 9.2

Druk \(x\) uit in \(y \text{.}\)

3p

\(y = 12 + 3 ⋅ {}^{5}\!\log(2 x + 8)\)

\(y = 12 + 3 ⋅ {}^{5}\!\log(2 x + 8)\)
\(3 ⋅ {}^{5}\!\log(2 x + 8) = y - 12\)
\({}^{5}\!\log(2 x + 8) = \frac{1}{3} y - 4\)

1p

\(2 x + 8 = 5^{\frac{1}{3} y - 4}\)

1p

\(2 x = 5^{\frac{1}{3} y - 4} - 8\)
\(x = \frac{1}{2} ⋅ 5^{\frac{1}{3} y - 4} - 4\)

1p

00ks 00kt 00kr 00ko 00kp 00kq 00l0 00l2 00l3 00l1 00kn