Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 1/e^2

The natural logarithm, denoted as 'ln', is the logarithm to the base 'e', where 'e' is an irrational constant approximately equal to 2.71828. It is used to solve equations involving exponential growth or decay. The natural logarithm has unique properties, such as ln(e) = 1 and ln(1) = 0, which are essential for simplifying expressions.

An exponential function is a mathematical function of the form f(x) = a * e^(bx), where 'a' and 'b' are constants, and 'e' is the base of the natural logarithm. This function describes growth or decay processes, such as population growth or radioactive decay. Understanding how to manipulate and evaluate exponential functions is crucial for solving logarithmic equations.

Logarithms have several key properties that simplify calculations, including the product, quotient, and power rules. For example, ln(a * b) = ln(a) + ln(b) and ln(a/b) = ln(a) - ln(b). These properties allow for the transformation of complex logarithmic expressions into simpler forms, making it easier to solve equations involving logarithms.