Mastering The Inverse Of Ln X: Its Range, Notations, And Use Of Natural Exponential Function

The function lnxis strictly ___________on (0,∞) and so has an inverse denoted by ln−1xor by_____________________.

increasing; e^x

The function ln x is strictly increasing on (0,∞), which means that for any values of x and y in (0, ∞) such that x < y, ln(x) < ln(y). This also implies that ln(x) takes every value in its range exactly once. Thus, the function has an inverse defined on its range, which is the set of all positive real numbers. The inverse of ln x can be denoted either as ln^-1 x or exp(x), where exp(x) is the natural exponential function. These two notations are equivalent and interchangeable. So, for any value y in the range of ln x, we could say either ln^-1 y or exp(y) to refer to the unique value of x that satisfies ln x = y.

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