Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 84 - ln 17

Key Concepts

Natural Logarithm

The natural logarithm, denoted as 'ln', is the logarithm to the base 'e', where 'e' is approximately equal to 2.71828. It is a fundamental concept in calculus and algebra, often used to solve equations involving exponential growth or decay. Understanding how to manipulate natural logarithms is essential for simplifying expressions and solving logarithmic equations.

Properties of Logarithms

Logarithms have several key properties that simplify calculations. One important property is the difference of logarithms: ln(a) - ln(b) = ln(a/b). This property allows us to convert the subtraction of two logarithms into the logarithm of a quotient, making it easier to compute values and solve equations involving logarithms.

Approximation and Rounding

In mathematics, approximation refers to finding a value that is close to, but not exactly equal to, a given number. Rounding is a common method of approximation, where numbers are adjusted to a specified number of decimal places. In this context, providing an approximation to four decimal places means expressing the final answer with four digits after the decimal point, which is important for precision in calculations.