Logarithms were invented by Baron John Napier in 1614. If you input a number N into the logarithm function, it outputs a number x which solves the following equation

10^x = N

Multiply the input by 10 means adding 1 to the output.

But we needn't choose 10 to raise to the power x. Choosing different numbers gives logarithms to different bases. For example, logarithms to the base 2 involves solving a different problem. x=Log₂(128) is a number which solves the following equation

2^x=128.

So Log₂(128)=7.

Gauss's prime number dice function goes up by 2.3 every time I multiply by 10. The logarithm behind this function is to the base of a special number called e=2.718281828459…

Click here to see how Gauss used the logarithm function to predict how many primes there are less than N