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

Key Concepts

Natural Logarithm (ln)

The natural logarithm, denoted as 'ln', is the logarithm to the base 'e', where 'e' is 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 and solving logarithmic equations.

Logarithmic Properties

Logarithmic properties are rules that simplify the manipulation of logarithmic expressions. Key properties include the product rule (ln(a*b) = ln(a) + ln(b)), the quotient rule (ln(a/b) = ln(a) - ln(b)), and the power rule (ln(a^b) = b*ln(a)). Understanding these properties is crucial for breaking down complex logarithmic expressions into simpler components.

Approximation Techniques

Approximation techniques involve estimating values that may not be easily calculable. In the context of logarithms, this often means using a calculator to find a numerical value to a specified number of decimal places. For example, when calculating ln(98/13), one would compute the exact value and then round it to four decimal places for clarity and precision in reporting results.