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 \(y = 660 x^{-1{,}13}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\)
Geef \(a\) in twee decimalen.

\(y = 660 x^{-1{,}13}\)
\(\log(y) = \log(660 x^{-1{,}13})\)

1p

\(\log(y) = \log(660) + \log(x^{-1{,}13})\)
\(\log(y) = \log(660) - 1{,}13 ⋅ \log(x)\)

1p

\(\log(y) = 2{,}819... - 1{,}13 ⋅ \log(x)\)
Dus \(y = 2{,}82 - 1{,}13 ⋅ \log(x) \text{.}\)

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 \(y = {90 \over x^{4}}\) in de vorm \(\log(y) = a + b ⋅ \log(x) \text{.}\)
Geef \(a\) in twee decimalen.

\(y = {90 \over x^{4}} = 90 x^{-4}\)
\(\log(y) = \log(90 x^{-4})\)

1p

\(\log(y) = \log(90) + \log(x^{-4})\)
\(\log(y) = \log(90) - 4 ⋅ \log(x)\)

1p

\(\log(y) = 1{,}954... - 4 ⋅ \log(x)\)
Dus \(y = 1{,}95 - 4 ⋅ \log(x) \text{.}\)

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 \(\log(y) = 3{,}35 - 1{,}52 ⋅ \log(x)\) in de vorm \(y = a x^{b} \text{.}\)
Geef \(a\) in gehelen.

\(\log(y) = 3{,}35 - 1{,}52 ⋅ \log(x)\)
\(\log(y) = \log(10^{3{,}35}) + \log(x^{-1{,}52})\)
\(\log(y) = \log(10^{3{,}35} ⋅ x^{-1{,}52})\)

1p

\(y = 10^{3{,}35} ⋅ x^{-1{,}52}\)

1p

\(y = 2238{,}721... ⋅ x^{-1{,}52}\)
Dus \(y = 2\,239 ⋅ x^{-1{,}52} \text{.}\)

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 \(y = 2\,300 ⋅ 0{,}86^{x}\) in de vorm \(\log(y) = a x + b \text{.}\)
Geef \(a\) in vier decimalen en \(b\) in twee decimalen.

\(y = 2\,300 ⋅ 0{,}86^{x}\)
\(\log(y) = \log(2\,300 ⋅ 0{,}86^{x})\)
\(\log(y) = \log(2\,300) + \log(0{,}86^{x})\)

1p

\(\log(y) = \log(2\,300) + x ⋅ \log(0{,}86)\)

1p

\(\log(y) = 3{,}361... + x ⋅ -0{,}06550...\)
Dus \(\log(y) = -0{,}0655 x + 3{,}36\)

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 \(y = 7\,600 ⋅ 1{,}25^{5 x + 2}\) in de vorm \(\log(y) = a x + b \text{.}\)
Geef \(a\) in vier decimalen en \(b\) in twee decimalen.

\(y = 7\,600 ⋅ 1{,}25^{5 x + 2}\)
\(\log(y) = \log(7\,600 ⋅ 1{,}25^{5 x + 2})\)
\(\log(y) = \log(7\,600) + \log(1{,}25^{5 x + 2})\)

1p

\(\log(y) = \log(7\,600) + (5 x + 2) ⋅ \log(1{,}25)\)
\(\log(y) = \log(7\,600) + 5 x ⋅ \log(1{,}25) + 2 ⋅ \log(1{,}25)\)

1p

\(\log(y) = 3{,}880... + 5 x ⋅ 0{,}09691... + 2 ⋅ 0{,}09691...\)
\(\log(y) = 3{,}880... + 0{,}48455... ⋅ x + 0{,}19382...\)
Dus \(\log(y) = 0{,}4846 x + 4{,}07\)

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 \(\log(y) = -0{,}4435 x + 1{,}16\) in de vorm \(y = b ⋅ g^{x} \text{.}\)
Geef \(b\) in gehelen en \(g\) in twee decimalen.

\(\log(y) = -0{,}4435 x + 1{,}16\)
\(y = 10^{-0{,}4435 x + 1{,}16}\)

1p

\(y = 10^{-0{,}4435 x} ⋅ 10^{1{,}16}\)
\(y = (10^{-0{,}4435})^{x} ⋅ 10^{1{,}16}\)

1p

\(y = 0{,}360...^{x} ⋅ 14{,}454...\)
Dus \(y = 14 ⋅ 0{,}36^{x} \text{.}\)

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 \(y = 1{,}84 ⋅ {}^{2}\!\log(x) + 1{,}14\) in de vorm \(y = {}^{2}\!\log(a x^{b}) \text{.}\)
Geef \(a\) en \(b\) in twee decimalen.

\(y = 1{,}84 ⋅ {}^{2}\!\log(x) + 1{,}14\)
\(\text{ } = {}^{2}\!\log(x^{1{,}84}) + 1{,}14\)

1p

\(\text{ } = {}^{2}\!\log(x^{1{,}84}) + {}^{2}\!\log(2^{1{,}14})\)
\(\text{ } = {}^{2}\!\log(x^{1{,}84} ⋅ 2^{1{,}14})\)

1p

\(\text{ } = {}^{2}\!\log(x^{1{,}84} ⋅ 2{,}203...)\)
Dus \(y = {}^{2}\!\log(2{,}20 ⋅ x^{1{,}84}) \text{.}\)

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 \(y = {}^{5}\!\log(1{,}8 x) - 1{,}4\) in de vorm \(y = a + b ⋅ {}^{3}\!\log(x) \text{.}\)
Geef \(a\) en \(b\) in twee decimalen.

\(y = {}^{5}\!\log(1{,}8 x) - 1{,}4\)
\(\text{ } = {}^{5}\!\log(1{,}8) + {}^{5}\!\log(x) - 1{,}4\)

1p

\(\text{ } = {}^{5}\!\log(1{,}8) - 1{,}4 + {{}^{3}\!\log(x) \over {}^{3}\!\log(5)}\)
\(\text{ } = {}^{5}\!\log(1{,}8) - 1{,}4 + {1 \over {}^{3}\!\log(5)} ⋅ {}^{3}\!\log(x)\)

1p

\(\text{ } = 0{,}365... - 1{,}4 + {1 \over 1{,}464...} ⋅ {}^{3}\!\log(x)\)
\(\text{ } = -1{,}034... + 0{,}682... ⋅ {}^{3}\!\log(x)\)
Dus \(y = -1{,}03 + 0{,}68 ⋅ {}^{3}\!\log(x) \text{.}\)

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 \(y = 5 ⋅ \log(400 x) - 6\) in de vorm \(y = a + b ⋅ \log(4 x) \text{.}\)

\(y = 5 ⋅ \log(400 x) - 6\)
\(\text{ } = 5 ⋅ (\log(100) + \log(4 x)) - 6\)

1p

\(\text{ } = 5 ⋅ (2 + \log(4 x)) - 6\)

1p

\(\text{ } = 10 + 5 ⋅ \log(4 x) - 6\)
\(\text{ } = 4 + 5 ⋅ \log(4 x)\)

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 \(y = {}^{2}\!\log({55 \over x^{3}})\) in de vorm \(y = a + b ⋅ {}^{2}\!\log(x) \text{.}\)
Geef \(a\) in twee decimalen.

\(y = {}^{2}\!\log({55 \over x^{3}})\)
\(\text{ } = {}^{2}\!\log(55 x^{-3})\)

1p

\(\text{ } = {}^{2}\!\log(55) + {}^{2}\!\log(x^{-3})\)
\(\text{ } = {}^{2}\!\log(55) - 3 ⋅ {}^{2}\!\log(x)\)

1p

\(\text{ } = 5{,}781... - 3 ⋅ {}^{2}\!\log(x)\)
Dus \(y = 5{,}78 - 3 ⋅ {}^{2}\!\log(x) \text{.}\)

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

\(y = 10 + 2 ⋅ {}^{9}\!\log(8 x - 4)\)

\(y = 10 + 2 ⋅ {}^{9}\!\log(8 x - 4)\)
\(2 ⋅ {}^{9}\!\log(8 x - 4) = y - 10\)
\({}^{9}\!\log(8 x - 4) = \frac{1}{2} y - 5\)

1p

\(8 x - 4 = 9^{\frac{1}{2} y - 5}\)

1p

\(8 x = 9^{\frac{1}{2} y - 5} + 4\)
\(x = \frac{1}{8} ⋅ 9^{\frac{1}{2} y - 5} + \frac{1}{2}\)

1p

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