eli5: What exactly is a logarithm?
In: Mathematics
After we first came up with the idea of addition, we realized that there had to also be a ‘reverse’ operation, which would require us to ‘work backwards’ from an addition. An addition question would be “3 plus 5 equals what?” A subtraction question, then, could be expressed as “3 plus what equals 5?”
Later on we developed this operation called multiplication, which can be understood as repeated addition. “5 x 3”, means “5 + 5 + 5”. And this operation, multiplication, could have a ‘reverse’ version too! We call that division. A multiplication question is “3 times 5 equals what?”, and a division question is “3 times what equals 5?”
Now, exponentiation is repeated multiplication just like multiplication is repeated addition. “3^5” means “3x3x3x3x3” And a logarithm is *its* reverse operation. Log_3(5) is asking “3 to the what equals 5?”
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