The logarithm function. If y = bx, then x = by is the inverse --> y = logb(x). If b = 10, then the function is often stated with the '10' implied: just log(x). For natural logarithms (y = ex), the function y = ln(x) [which indicates loge(x)] is the inverse.
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No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.
An exponential function is of the form y = a^x, where a is a constant. The inverse of this is x = a^y --> y = ln(x)/ln(a), where ln() means the natural log.
The inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain. The domain of a function is the range of the inverse function. The range of a function is the domain of the inverse function.
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One is the inverse of the other, just like the arc-sine is the inverse of the sine, or division is the inverse of multiplication.