how does e raised to the natural log of x  equal x

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By definition the natural log (ln) of a number is the exponent needed to raise e to that number.Or, ln(x) = y means that e^y = xSo, e^(ln(x)) = x

The exponential function y = e^x is the inverse function of the natural logarithmic function y = ln(x).  Essentially, they "undo" each other (much like division and multiplication undo each other). So e^(ln(x)) = x and ln(e^x) = x