Logarithmic and Exponential Functions is usually met around Secondary 3 A-Math — though schools sequence topics differently — and is covered in Odyssey Math Tuition’s online math course for that level, with recorded video lessons, a question bank, topical practice and a topical test. Most marks lost here come from execution errors rather than misunderstanding, which is why targeted practice works.
What logarithmic and exponential functions actually asks of a student
A logarithm answers the question “what power?” If two to the power of something gives eight, the logarithm base two of eight is three. Exponential functions are the same relationship read the other way round.
Students who hold that sentence firmly find the topic manageable. Students who memorise the laws without it tend to apply them in impossible places, which is where most of the lost marks come from.
What the topic assumes you already have
Most difficulty in this topic is not caused by the topic itself. It is caused by something earlier that never became fluent. Check these first:
- Index laws, completely fluent — logarithm laws mirror them
- Solving equations by rearrangement
- Comfort with negative and fractional powers
- Understanding that a logarithm of a negative number has no real value
If any of these is shaky, repair it before going further. Working on new material while a prerequisite is unstable is how students spend hours and move nothing.
Where marks are actually lost
- Treating log(a + b) as log a + log b, which is not a law and never has been
- Changing base incorrectly, or forgetting that a change of base is needed
- Solving an exponential equation without taking logarithms of both sides
- Producing a solution that makes the argument of a logarithm negative and not rejecting it
- Losing the base when writing intermediate lines
Most of these are execution errors rather than gaps in understanding, which is encouraging: they respond to practice and to keeping a written record of the mistakes you personally repeat.
A revision approach that works
- Write each logarithm law next to its matching index law. Seeing them paired makes both stick.
- Check every solution against the domain — arguments must be positive.
- Practise converting between exponential and logarithmic form until it is automatic.
- Do a mixed set; blocked practice hides which law is not understood.
How the Secondary 3 A-Math course covers it
In the Secondary 3 A-Math online course this topic follows the same shape as every other: a recorded explanation, a question bank with answers worked through rather than printed, topical practice, and a topical test. Lessons are recorded personally by our founder, Mr. Justin Tan, and the course follows our own curriculum, aligned to the MOE syllabus.
The courses also include past-year school examination papers with worked answers, which shows how a topic is actually examined rather than how it is taught. Access is 24 hours a day with unlimited replays, and every online course carries a 7-day money-back guarantee.
Where this sits in the wider syllabus
For the year as a whole, see our guide to this stage. For the subject in context, this guide and this one cover what comes before and after.
Syllabus details follow Ministry of Education and SEAB published documents. Course details and prices are as published at the time of writing — check the course pages for current information. We do not promise grades.
Read next
Related reading on studying maths online: Arc Length and Sector Area: A Secondary 3 E-Math Guide, Functions and Graphs: A Secondary 3 E-Math Guide, Trigonometric Identities and Equations: A Sec 3 A-Math Guide, Equations of Tangent and Normal: A Sec 4 A-Math Guide, Inside the Junior College 1 H2 Mathematics Online Math Course, Statistics and Data Analysis: A Sec 4 E-Math Guide. On choosing a school at this stage, see our list of secondary schools in Singapore.
More on getting the most from your maths
Frequently asked questions
What does logarithmic and exponential functions cover at Secondary 3 A-Math?
A logarithm answers the question “what power?” If two to the power of something gives eight, the logarithm base two of eight is three. Exponential functions are the same relationship read the other way round.…
What should my child revise before this topic?
The prerequisites listed above. Most difficulty traces back to an earlier skill that never became fluent rather than to the topic itself.
Where do students lose the most marks?
Almost always in execution rather than understanding — sign errors, answering a different question from the one asked, or skipping the sketch.
Is this topic in the online course?
Yes. It is covered in the Secondary 3 A-Math online math course with video lessons, a question bank, topical practice and a topical test.
Can we access just this topic?
Yes. The courses are self-paced and non-linear, so a student can go straight to one topic without working through the rest.
Is there a trial period?
All online courses carry a 7-day money-back guarantee. The terms and conditions set out how it works.
Last reviewed July 2026. Syllabus details follow the Ministry of Education and SEAB published documents.
