Mathematics
What is A logarithm?
A logarithm answers the question 'how many times do I multiply this number to get that one?' It's the reverse of raising a number to a power, and it turns huge, fast-growing quantities into manageable scales — used in everything from earthquakes to sound.
See it, don’t just read it.
Watch a 2-minute lesson with voice + animation that explains a logarithm.
Key things to understand
- 1It's the inverse of raising a number to a power.
- 2The log (base 10) of 1000 is 3, because 10×10×10 = 1000.
- 3Logarithms compress huge ranges into small, readable numbers.
- 4The Richter scale, decibels, and pH are all logarithmic.
- 5They turn multiplication into addition, which once simplified hand calculation.
Frequently asked questions
- What is a logarithm in simple terms?
- It tells you the exponent: the logarithm of 1000 (base 10) is 3, because you multiply 10 by itself 3 times to get 1000.
- Why are logarithmic scales used?
- They squeeze enormous ranges — like earthquake energy or sound intensity — into a compact scale where each step means a big multiplication.
- What does a logarithmic scale mean for earthquakes?
- On the Richter scale, each whole number is about 10 times stronger shaking, so a magnitude 6 is roughly ten times a 5.