Zadanie 3b
Find k.
Rational powers and logarithm rules
Manipulate fractional powers and logarithms, change logarithm bases and solve exponential equations with valid domains.
Tę umiejętność sprawdzają 44 zadania wzorowane na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 44 Otwórz w wyszukiwarce z filtrami
Zadanie 3c
When does the reading reach 16°C?
Zadanie 4b
Hence solve (f∘g)(x) = 24.
Zadanie 4a
Given log2 p = 4 + log2 r, prove p=16r.
Zadanie 4b
Hence solve log2 p = 4 + log2 r and logr p = 5.
Zadanie 5a
For x > 0, prove log49(16x2) = log7 4 + log7 x.
Zadanie 5b
Hence solve for x > 0.
Zadanie 5a
Show that L6 = ln a and determine the positive integer a.
Zadanie 5b
Hence state L98.
Zadanie 9e
One play costs 6 credits. At least seven red markers win 50 credits, at least seven blue markers win B credits (a positive integer), and at least seven gold markers win 15 credits. Otherwise the prize is zero. These prize events are mutually exclusive. Let X…
Zadanie 9d
Prove that cₙ is arithmetic.
Zadanie 9e
Find the largest integer k for which C₂₄<0.
Zadanie 1a
Write ln 5 + ln 6 as ln k for a positive integer k.
Zadanie 1b
Write 2ln 7 as ln k for a positive integer k.
Zadanie 1c
Write −ln(1/9) as ln k for a positive integer k.
Zadanie 2a
Express log10 56 in terms of p and q.
Zadanie 2b
Express log7 16 in terms of p and q.
Zadanie 9a
Find f−1(9) as a fraction of integers.
Zadanie 9c
Show that (f∘g)(x) = 729x3.
Zadanie 5b
Hence or otherwise solve log3[x(x2 − 4)] − 1 = log3[(x2 − 11x + 18)(x + 2)].
Zadanie 6
Solve 3log27(6x) − log9 x = 1.
Zadanie 8b
Find the first complete month when F predicts at least 28000 accounts.
Zadanie 8c
Write F(t)=2400eᵏᵗ. Find k exactly.
Zadanie 9d
Hence show that .
Zadanie 2c
Find the least number n of complete years after which its value is below 15% of its original price.
Zadanie 3a
Find log5(1/a).
Zadanie 3b
Find log125 a.
Zadanie 3b
Hence or otherwise, solve 2 ⋅ 16x + 7 ⋅ 4x − 4 = 0 for real x.
Zadanie 4b
Find the attenuation score for D.
Zadanie 4c
Another configuration has attenuation score 86. Find its amplitude ratio.
Zadanie 7d
Solve f(x)=g(x), giving x in the form a+ln b with rational a,b.
Zadanie 9e
Suppose a=16 and s>0, and define un = An + ln Gn. (i) Show that u_n is arithmetic and find its common difference. (ii) Show that .
Zadanie 8a
Find (i) f(3); (ii) f(1/9).
Zadanie 8b
Find f−1(x).
Zadanie 8d
For x>0, obtain the graph of y = f(3x2) from y = log3 x using one translation and one stretch. Describe both transformations and their order.
Zadanie 8a
Find (i) f(25); (ii) f(1/25).
Zadanie 8b
Find f−1(x).
Zadanie 8d
For x>0, obtain the graph of y = f(125x3) from y = log5 x using one translation and one stretch. Describe both transformations and their order.
Zadanie 5
For x≥0, a region is bounded by y = 3x2/(x3 + 4), the x-axis and x=c, where c>0. Its area is ln3. Find c.
Zadanie 8b
(i) Show that intersection abscissas satisfy x2 − 3dx + 6d = 0. (ii) Hence show that 9d2 − 24d > 0. (iii) Find the possible values of d.
Zadanie 8b
(i) Show that intersection abscissas satisfy x2 − 3dx + 6d = 0. (ii) Hence show that 9d2 − 24d > 0. (iii) Find the possible values of d.
Zadanie 2a
State p.
Zadanie 8a
Evaluate (i)log3(1/27); (ii)log16 2; (iii).
Zadanie 8b
Positive u,v satisfy u/v≠1 and logu/v u = 4. (i) Show that logu/v v = 3. (ii) Hence find .