Log-log & semi-log graphs
Practice Flashcards
Flip to reveal answersWhich graph straightens a power law y = a·xⁿ?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Log-log & semi-log graphs
Sign up free to track progress and get spaced-repetition review schedules.
Question
Which graph straightens a power law y = a·xⁿ?
Answer
Log-log: plot log y against log x. It's straight, with gradient n and intercept log a.
Question
Which graph straightens an exponential law y = a·bˣ?
Answer
Semi-log: plot log y against x. It's straight, with gradient log b and intercept log a.
Question
Why take logs of y = a·xⁿ?
Answer
log y = log a + n·log x is LINEAR in log x, so a curved power law becomes a straight line you can read.
Question
On a log-log line for y = a·xⁿ, what is the gradient?
Answer
The power n.
Question
On a semi-log line for y = a·bˣ, what is the gradient?
Answer
log b (so b = 10^gradient).
Question
How do you recover a from a log-log or semi-log intercept?
Answer
The intercept is log a, so a = 10^(intercept).
Question
How do you choose between a power and an exponential model from data?
Answer
Linearise both ways and compare R² — the fit with R² closer to 1 is straighter, so that's the model.
Question
Semi-log gives gradient 0.3, intercept 2 for y = a·bˣ. Find a and b.
Answer
a = 10² = 100; b = 10^0.3 ≈ 2.00, so y ≈ 100·2ˣ.
Read the notes
Full study notes for Log-log & semi-log graphs
Topic 2.10 hub
Log-log & semi-log graphs (HL only)
More from Topic 2.10
All flashcards in this topic
Math AI exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free