Linear Law with Logarithms: Turning Models into Straight Lines

SAT Score Range

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1 session

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This series ended on December 1, 2025. All 1:1 and group chats related to this series are disabled 7 days after the last session.

About

In this one-session series, we will practise the A-level “linear law” technique: using logarithms to turn non-linear models into straight lines and then reading off parameters from the graph. We will work with equations such as y = Ax^n, y = Ae^{-kx^2}, 3^y = 4^{2−x}, and y = C(a^x). After taking logs, we will decide whether to plot ln y against ln x, ln y against x, or ln y against x^2, and then use the gradient and intercept of the straight line to estimate A, n, k, C, and a. The session will be very exam-style: I will briefly review the log rules, set up each question, give you time to try it, and then we will go through a clear step-by-step solution together.
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A recent graduate of CAIE A-levels with Mathematics, Physics, and Computer Science. Currently, pursuing my B.Sc. in Computer Science & Engineering. Passionate about math and education, I am eager to help others excel in subjects including math, physics, computer science, and SAT Prep. Excited to tutor in various math areas such as Algebra, Geometry, Pre-Calculus, Calculus, and Statistics. Let's learn and grow together!

Sessions

✋ ATTENDANCE POLICY

This is a problem-solving, exam-style session, so live participation is important. Please:

• Join on time and plan to stay for the full session.

• Be ready to work: have paper, pen/pencil, a calculator, and (if possible) squared/graph paper.

• Try each question yourself before we discuss the solution – it is okay to make mistakes.

• Keep chat and mic contributions respectful and on-topic.

SESSION 1

1

Dec

SESSION 1

Logarithms

Mon 4:00 AM - 5:00 AM UTCDec 1, 4:00 AM - 5:00 AM UTC

We will focus on A-level style “linear law” questions that use logarithms to turn models into straight lines and then estimate parameters from the graph.
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Plan:
• Quick warm-up on key log rules and straight-line form y = mx + c.  
• Take logs of models such as y = Ax^n and y = Ae^{-kx^2} to obtain equations like ln y = ln A + n ln x or ln y = ln A − kx^2.  
• Decide what to plot (ln y vs ln x, ln y vs x, or ln y vs x^2) so that the graph is a straight line.  
• Practise reading gradient and intercept from the line to find A, n, k, C, and a in equations like y = C(a^x).  
• Include at least one example where we show that an equation such as 3^y = 4^{2−x} leads to a straight line when plotted correctly, and interpret the gradient.  
• Throughout, we will use past-paper-style questions (from CAIE A Level 9709) and work through full, exam-ready solutions.
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By the end of the session, you should feel confident in setting up and solving linear-law questions using logarithms and straight-line graphs.

Public Discussion

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Dec 1

1 week

60 mins

/ session

SCHEDULE

Monday, Dec 1

4:00AM