An Easy and Intuitive Approach to Understanding Logarithms

If you are a secondary or JC student in Singapore, chances are you have already met logarithms in both Maths and Physics and also felt a little stuck. You are not alone. Many students say that logarithms feel abstract, confusing, and disconnected from real life. The good news? Logarithms are actually very logical, visual, and powerful once you understand what they are trying to do.

This article takes a calm, step-by-step approach to help you see logarithms differently especially in Physics so that they feel less intimidating and more meaningful.

What Are Logarithms Really Trying to Tell Us?

At its heart, a logarithmic function is not about memorising formulas. It is about comparison. Instead of asking, “How big is this number?”, logarithms ask:

“How many times bigger is this compared to something else?”

In Physics, many quantities change too fast or too slowly to be shown on a normal scale. This is where the logarithmic scale becomes useful. It helps us compress very large ranges into something we can understand and work with.

Why Physics Loves Logarithms

Physics uses logarithms because nature often behaves exponentially. Some classic examples you may recognise:

• Sound intensity (decibels)

• Earthquake strength (Richter scale)

• Light intensity

• Radioactive decay

When these are plotted, they form a logarithmic curve, not a straight line. Students often fear these curves because they look unfamiliar. But once you realise that each step on the axis represents multiplication, not addition, the graph starts to make sense.

For example, on a logarithmic scale:

• Moving from 10 to 100 is the same “distance” as moving from 100 to 1000

• Each step means “10 times bigger”, not “+10”

Sections Students Commonly Fear (and Why)

Let’s address the parts of logarithms that students most often struggle with.

1. Logarithmic Form vs Exponential Form

Many students get confused converting between forms:

• Exponential:
  102=100102=100

• Logarithmic form:
  log⁡10(100)=2log10​(100)=2

It helps to read logarithms as a question:

“10 raised to what power gives 100?”

Thinking in words first often reduces mistakes.

2. Logarithmic Identities

This is another major fear point. Students tend to memorise without understanding:

Instead of memorising, imagine logarithms as breaking big problems into smaller, manageable parts. In Physics, this helps simplify equations and make calculations easier—especially when dealing with powers of 10.

3. Interpreting Logarithmic Graphs

A logarithmic curve increases quickly at first, then slows down. Many students expect a straight line and panic when they don’t see one.

A helpful mindset:

• Steep at the start → rapid change

• Gradually flattening → slowing change

Once this visual idea clicks, interpreting graphs in Physics becomes far less stressful.

How Logarithms Connect Maths and Physics

Logarithms are one of the strongest bridges between Maths and Physics. When you understand them well in Maths, Physics formulas stop feeling random. Concepts like scale, rate of change, and comparison become clearer.

This is why strong foundations especially through guided Maths Tuition often make a noticeable difference. When students are encouraged to ask why a formula works instead of just applying it, confidence grows naturally.

A Final Thought

Logarithms are not meant to be scary. They are tools that help us understand a complex world in a simpler way. With the right explanation, plenty of visual thinking, and patient practice, what once felt confusing can become one of the most satisfying chapters in Maths and Physics.

If you’ve ever felt that logarithms were “just not for you”, it may simply be that you haven’t seen them explained in a way that matches how you learn. And once that happens, everything starts to fall into place.