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What is a logarithm?

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Quick answer

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.

Key things to understand

  1. It's the inverse of raising a number to a power.
  2. The log (base 10) of 1000 is 3, because 10×10×10 = 1000.
  3. Logarithms compress huge ranges into small, readable numbers.
  4. The Richter scale, decibels, and pH are all logarithmic.
  5. They turn multiplication into addition, which once simplified hand calculation.

People also ask

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.
Where are logarithms used?
Measuring earthquakes (Richter), sound (decibels), acidity (pH), and in algorithms and growth rates.
What is a natural logarithm?
A logarithm with base e (≈2.718), common in math and science for continuous growth.