ELI5: logarithms

What is a logarithm?

A logarithm is like asking "how many times do I multiply a number by itself to get another number?" [1] For example, if you want to know how many times you multiply 10 by itself to get 1,000, the answer is 3 (because 10 × 10 × 10 = 1,000), so the logarithm is 3. [1]

Why would you use it?

Before calculators, people used logarithms to make really hard multiplication and division problems much easier. [5] Instead of multiplying big numbers together, you could use logarithms to turn multiplication into addition, which is way faster. [5]

How do you read it?

When you see "log₁₀(1,000) = 3," you're reading it as "the logarithm of 1,000 to the base 10 equals 3." [1] The base (10) is the number you keep multiplying, and 3 is how many times you multiply it to get 1,000. [1]

Where do you see it?

Logarithms show up everywhere in science, like measuring how loud sounds are or how acidic something is. [1] They help us understand things that grow or shrink really fast, like population growth or radioactive decay. [1]