Log is non-monotonic in PHP and Lua

The binary logarithm can be computed faster and more accurately, except for arguments very close to 1.

It is a historical accident that most standard libraries have been defined in the past to include natural logarithms instead of binary logarithms. Moreover lazy implementers sometimes have written a binary logarithm function that uses a pre-existing hyperbolic logarithm function, instead of the direct implementation that would be much more efficient.

Derivatives and primitives are seldom computed, but the computational advantage of binary logarithms applies to each function evaluation.

Even when derivatives or primitives are computed, in almost all applications there already exists another multiplicative constant in the formula that must be computed, which can absorb in it the factor "ln 2", so there is no increased computational cost.

There exists absolutely no reason to ever use multiple bases with logarithms.

One can choose to always use only binary logarithms and there exists no problem that would need other kinds of logarithms.

Choosing a base for logarithms is equivalent with choosing a unit of measurement for them. Changing the base of logarithms is done by the same rules as changing the unit of measurement for any quantity. In the same way as there is no need to use multiple units of measurement for a quantity, there is no need to ever work with multiple bases for logarithms.

Thus there is no reason for a programming language to include a function with 2 arguments like "log(arg, base)" instead of having only a function with 1 argument, e.g. "log2" (and the 2 constants LN_2 and LOG2_E).

If someone had the weird idea to write some formula with logarithms in a random base they should convert that formula to use binary logarithms, because there is no advantage in using another base.

Nonetheless, if one would want to include such a function, or any other function, one could reduce the argument to some small range using mathematical properties of the function and then some polynomial approximation should be determined, in order to use it to compute the function values.

If you determine a polynomial approximation for a function, whichever function it is, you can compute the entire function faster and more accurately than when you compute the function as a composition of other functions, one or more of which are computed by their own polynomial approximations.

In order to ensure that the function is rounded correctly, one must determine how many polynomial terms are needed and how big must be the numbers used for storing the coefficients.

For a function with a single argument, like "log2", it is much easier to do an exhaustive search to find all the argument values that would need more polynomial terms or more bits in the coefficients, to guarantee correct rounding.

For functions with 2 arguments, it can be difficult or impossible to find all problematic argument pairs, unless the function has some special mathematical properties that would allow a formal proof about the accuracy needed in polynomial evaluation to ensure correct rounding.