Custom Logarithm Lua (Answer has trick that can be used on almost any language)

Question

I'm working on a base converter for lua that can convert the base of any number to another base. For that, I need a logarithm calculator. Example function (where logarithm(100, 10) would equal log₁₀(100), which would equal 2):

function logarithm(value, base)
    ... -- Algorithm here
end
print(logarithm(100, 10))

Which would output:

2

P.S: I want the algorithm to accept any base, any value.

Answer 1

You can always use that

log_b(a) = log_c(a) / log_c(b)

where c is one of the provided bases, like the Euler number e of the natural logarithm or 10, sometimes also the basis 2 logarithm is provided.