Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 28

Verified step by step guidance

1. Recognize that 'ln' refers to the natural logarithm, which is the logarithm to the base 'e', where 'e' is approximately 2.71828.
2. Understand that the problem is asking for the natural logarithm of 28, which can be expressed as \( \ln(28) \).
3. To find \( \ln(28) \), you can use a calculator that has a natural logarithm function, often labeled as 'ln'.
4. Enter the number 28 into the calculator and press the 'ln' button to compute the natural logarithm.
5. If an approximation is needed, round the result to four decimal places as specified in the problem.

Key Concepts

Natural Logarithm (ln)

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 and is particularly important in calculus and complex analysis. The natural logarithm has unique properties, such as ln(e) = 1 and ln(1) = 0, which are essential for simplifying expressions.

Exponential Functions

Exponential functions are mathematical functions of the form f(x) = a * e^(bx), where 'a' and 'b' are constants, and 'e' is the base of natural logarithms. These functions model growth or decay processes, such as population growth or radioactive decay. Understanding how to manipulate and evaluate these functions is crucial for solving problems involving natural logarithms.

Approximation Techniques

Approximation techniques are methods used to estimate values that may not be easily calculable or are irrational, such as logarithms of non-integer values. In the context of logarithms, this often involves using calculators or numerical methods to find values to a specified degree of accuracy, such as four decimal places. Mastery of approximation techniques is essential for practical applications in science and engineering.