Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 98 - ln 13

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 Techniques

In many mathematical contexts, especially when dealing with logarithmic values, approximation techniques are used to express results to a specified number of decimal places. For instance, using a calculator or logarithm tables, one can find the approximate value of ln(98) - ln(13) and round it to four decimal places, which is often necessary for practical applications in science and engineering.