To evaluate the expression e ln 5, we can utilize the properties of logarithms and exponents. In general, the natural logarithm (ln) is the inverse function of the exponential function with base e. This means that when we raise e to the power of the natural logarithm of a number, we essentially ‘undo’ the logarithm.
In mathematical terms, we have:
- e ln x = x for any positive number x.
Applying this to our specific case:
- Let x = 5.
- Thus, e ln 5 = 5.
So, the value of e ln 5 is simply 5.