eli5: What exactly is a logarithm?

Question

eli5: What exactly is a logarithm?

In: Mathematics

Answer 1

There is addition. And when you add the same thing many times, it becomes quickly annoying:

2 + 2 + 2 + 2 = 8

So we have multiplication.

2 × 4 = 8

And we can determine how many additions were performed, using division:

3 × n = 27

n = 27 ÷ 3

—–

There is multiplication. And when you multiply the same thing many times, it becomes quickly annoying:

2 × 2 × 2 × 2 = 16

So we have exponentiation.

2⁴ = 16

And we can determine how many multiplications were performed, using *logarithms*:

3ⁿ = 27

n = log₃(27)

—–

Just like a division will not always give you whole numbers (7÷3 for instance), and it might seem absurd to perform an addition a non-integer number of times, logarithms will not always you give you whole numbers and it appears equally absurd.