Simplifying the Expression lne^x: Understanding the Properties of ln and e^x

lne^x

To simplify the expression lne^x, we need to understand the properties of the natural logarithm function (ln) and the exponential function (e^x)

To simplify the expression lne^x, we need to understand the properties of the natural logarithm function (ln) and the exponential function (e^x).

The natural logarithm function, ln(x), is the inverse function of the exponential function e^x. In other words, ln(e^x) = x. This means that the natural logarithm of e raised to any power will give us that power, or in this case, ln(e^x) = x.

Now let’s apply this to the expression lne^x. Since e^x is the base of the natural logarithm function, ln(e^x) simplifies to just x. Therefore, lne^x = x.

In summary, the expression lne^x simplifies to x.

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