Math: If the opposite of doing x^2 is rad(x), what is the opposite of log(x)?

Question

What about opposite of 2^x and x!?

Answer 1

x^2 and √x are inverse operations, when x is nonnegative. That is:

√(x^2) = x, when x is nonnegative

(√x)^2 = x, when x is nonnegative

If by log(x), you mean the base-10 logarithm, then log (x) and 10^x are inverse operations, when x is positive. That is:

10^(log x) = x, when x is positive

log (10^x) = x.

The factorial doesn't really have an inverse operation.

The inverse operation of 2^x is log2 (x) ("log base 2" of x).

Answer 2

The inverse operation of a logarithm is exponentiation.  Using your example, the inverse operation essentially cancels itself out.

sqrt(x^2) = x

log(x), in most calculators, assumes a base of 10, also written as log10(x).  

10^log10(x) = x

Some other calculators assume a base of e (eulers number or constant), in which case the inverse operation would be

e^loge(x) = x

Answer 3

Exponential (x), abbreviated exp(x).  It is necessary to distinguish the base of the logarithm; there are two such in common use: 10, and a number called e whose value is 2.71828...  The latter shows up frequently in advanced mathematics.  There is no common designation for an inverse factorial, but if y = 2^x, then x = log2(y) -- which is an example of a logarithm which isn't either base 10 or base e.