The value of e^ln(x) is x. This is because ln(x) is the inverse function of e(x), which means that applying the function f(x) = e^x reverses the effect of the function f(x) = ln(x).
The definition of the natural logarithm ln(x) is that it is the area under the curve y = 1/t between t = 1 and t = x. As a result, the value of ln(e) is 1. Since e^ln(x) = x, the graph of the function y = e^ln(x) is a straight line through the origin with a gradient of 1. It has the line equation y = x.