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Chapter 10: Problem 19

Find each logarithm. Give approximations to four decimal places. \(\ln 388.1\)

Short Answer

Expert verified
The natural logarithm of 388.1 is approximately 5.9610.

Step by step solution

01

- Understand the problem

The problem asks to find the natural logarithm of 388.1, which is denoted as \(\backslash \text{ln }388.1\). The natural logarithm is the logarithm to the base e, where e is approximately 2.71828.
02

- Use a scientific calculator

To find \( \backslash \text{ln }388.1 \), use a scientific calculator. Most scientific calculators have a \(\backslash \text{ln}\) button.
03

- Input the number

Press the \(\backslash \text{ln}\) button and then enter 388.1 on the calculator. This will compute the natural logarithm of 388.1.
04

- Record the result

Read the result displayed on the calculator. Ensure the answer is approximated to four decimal places.
05

- Verifying the result

Double-check the approximation by performing the calculation again, if necessary, to ensure accuracy.

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Key Concepts

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

Logarithms
Logarithms are mathematical functions that help us determine how many times a certain number, called the base, must be multiplied by itself to reach another given number. There are various types of logarithms, such as common logarithms (base 10) and natural logarithms (base e). The natural logarithm, denoted as \( \ln \), uses the base e, which is approximately 2.71828. In this exercise, you are asked to find the natural logarithm of 388.1.
Scientific Calculator
A scientific calculator is essential for solving logarithmic functions, especially those involving natural logarithms. Most scientific calculators have a dedicated \( \ln \) button. Here is how to use it for finding \( \ln 388.1 \):
  • Turn on your calculator and locate the \( \ln \) button.
  • Press the \( \ln \) button first or after entering the number, depending on your calculator's design.
  • Enter 388.1 into the calculator.
  • The calculator will display the natural logarithm of 388.1, which you should then approximate to four decimal places.
Always double-check your result to ensure accuracy.
Approximation
Approximation is the process of finding a value that is close enough to the correct answer for practical purposes. In mathematical calculations, approximations are often necessary when dealing with irrational numbers or when the exact value is not needed. When you calculated \( \ln 388.1 \) using your scientific calculator, you obtained a result that should be approximated to four decimal places. This means rounding the number to maintain only four digits after the decimal point. For example, if your calculator shows 5.960713, you would round this to 5.9607. Consistently approximating to four decimal places ensures standardized and easily comparable results.

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Most popular questions from this chapter

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