Problem 11 Use a calculator to find each of... [FREE SOLUTION]

Chapter 12: Problem 11

Use a calculator to find each of the following to four decimal places. $$ \ln 5 $$

Short Answer

Expert verified

1.6094

Step by step solution

- Understand the problem

The task is to find the natural logarithm of the number 5, represented as $\text{ln} 5$, and to round it to four decimal places.

- Use a calculator

Turn on your calculator. Locate the 'ln' button, which represents the natural logarithm function. Enter the number 5 and then press the 'ln' button.

- Note the result

The calculator will display the value of $\text{ln} 5$. Write down the number shown on the screen. It should be approximately 1.609437912.

- Round to four decimal places

Round the result from Step 3 to four decimal places. The digit following the fourth decimal place (9) is 3, which means we do not need to round up.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

calculator usage

Using a calculator for solving logarithmic functions can simplify complex mathematical problems. First, ensure your calculator is in the correct mode by turning it on and locating the 'ln' button, which stands for the natural logarithm. Key in the number you wish to find the logarithm of, in this case, 5. Then, press the 'ln' button. This will yield the natural logarithm of 5. Calculators with this function are very handy tools in mathematics and can help you quickly find precise results.

rounding numbers

Rounding numbers is an essential skill for dealing with real-world applications of mathematics. When rounding to a specific decimal place, it's important to follow these steps: Identify the digit at the place you need to round to; in this exercise, it's the fourth decimal place. Look at the digit immediately to the right of it. If this digit is 5 or higher, round up the fourth decimal place by one. If it's lower than 5, keep the digit in the fourth decimal place the same. For instance, rounding 1.609437912 to four decimal places, we check the fifth digit (3). Since 3 is less than 5, we retain the fourth digit as 9, resulting in 1.6094.

ln function

The natural logarithm, denoted as $ \text{ln} $, is a logarithm to the base of the mathematical constant e (approximately 2.71828). In mathematical terms, $ \text{ln}(x) $ represents the power to which e must be raised to obtain the number x. It's widely used in various fields such as physics, finance, and statistics. For example, the natural logarithm of 5 ($ \text{ln}(5) $) is approximately 1.6094 when rounded to four decimal places. Understanding the $ \text{ln} $ function is crucial for comprehending exponential growth and decay processes.

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91影视

Use a calculator to find each of the following to four decimal places. $$ \ln 5 $$

Short Answer

Step by step solution

- Understand the problem

- Use a calculator

- Note the result

- Round to four decimal places

Key Concepts

calculator usage

rounding numbers

ln function

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