Teaching Logs – I was Born BC (Before Calculators!)

 

Teaching Logs – Born BC (Before Calculators!)

There was a time—believe it or not—when doing a multiplication like 347 × 82 wasn’t a quick tap on a calculator… it was a mini project.

Yes, I was born BC – Before Calculators.

And in those days, we had two magical tools:

• Logarithm tables
• Slide rules

Both built on one brilliant idea:
Turn difficult calculations (multiplication/division) into easier ones (addition/subtraction)

---

The Big Idea – Why Logs Work

The key comes from the mathematical rule:

log(a × b) = log(a) + log(b)
log(a ÷ b) = log(a) − log(b)

So instead of multiplying two awkward numbers, we:

1. Look up their logs in a table
2. Add them together
3. Convert (antilog) back to get the answer

Simple… well… eventually simple 

---

📖 Logarithm Tables – The Original “Calculator App”

A book of log tables was an essential bit of kit—right up there with a pen and ruler.

To multiply numbers:

• Look up the log of each number
• Add the values (carefully!)
• Use the antilog table to convert back

Sounds straightforward… until:

• You misread a row
• Add incorrectly
• Or forget where the decimal point should go (a favourite mistake!)

But once mastered, it was fast and surprisingly accurate.

---

📏 Slide Rules – The Engineer’s Superpower

 The slide rule—a beautifully simple analogue computer.

Instead of looking up numbers, the slide rule:

• Uses logarithmic scales
• Lets you physically add lengths (which represent logs)
• Gives you the answer instantly by lining things up

No batteries. No screen. No fuss.

Engineers used them to:

• Design bridges
• Calculate trajectories
• Even help send humans to the Moon 

And all with a bit of sliding wood or plastic!

---

Why Bother?

You might ask: why go through all this trouble?

Because:

• Multiplication and division are harder operations
• Addition and subtraction are much easier
• Logs convert one into the other

It’s a brilliant example of mathematics simplifying the world

---

Teaching Today – What We’ve Lost (and Gained)

Today’s students:

• Have powerful calculators
• Can compute instantly
• But sometimes miss the why behind the maths

Back then, you:

• Understood place value deeply
• Estimated answers before calculating
• Developed a real “feel” for numbers

And perhaps most importantly…
You appreciated just how clever mathematics really is

---

Final Thought

When I tell students today about log tables and slide rules, I usually get that look…

“Sir… you actually did maths like that?”

Yes. Yes we did.

And somehow… we survived.