/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Use a calculator to find each of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 12

Use a calculator to find each of the following to four decimal places. $$ \ln 2 $$

Short Answer

Expert verified
\text{\textbackslash}{\function(2)\textbackslash} \result\text{is\textbackslash{0.6931}\textbackslash{to}\textbackslash%{four\textbackslash%{decimal\textbackslash%{places\textbackslash%.}

Step by step solution

01

- Understand the Problem

The problem requires finding the natural logarithm of 2 to four decimal places. The natural logarithm is the logarithm to the base e, where e is approximately 2.71828.
02

- Use a Calculator

Turn on the scientific calculator and locate the 'ln' function, which represents the natural logarithm.
03

- Enter the Value

Input the number 2 and then press the 'ln' button to calculate the natural logarithm of 2.
04

- Read and Round the Result

The calculator will display the result. Read the value and round it to four decimal places.
05

- Write the Final Answer

Write down the rounded result. Ensure it has exactly four decimal places.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Scientific Calculator
To solve problems involving natural logarithms, a scientific calculator is essential. This type of calculator has functions that are specifically designed for advanced mathematical operations, such as finding logarithms.
To use a scientific calculator for our problem, start by turning it on. Next, locate the 'ln' button, which stands for natural logarithm. This button is often grouped with other logarithmic functions. By pressing the 'ln' button after entering the number, you will find the natural logarithm value displayed instantly.
Rounding Decimals
Rounding decimals is a crucial skill to ensure answers conform to specified precision levels, such as four decimal places. Here鈥檚 how to round a number to four decimal places:
  • First, identify the digit in the fourth decimal place.
  • Next, look at the digit immediately to the right (the fifth decimal place).
  • If this digit is 5 or greater, round up the fourth decimal place by one. If it is less than 5, leave the fourth decimal place as is.

For example, when rounding 0.693147 to four decimal places, the digit in the fourth place is 1, and the digit in the fifth place is 4. Since 4 is less than 5, we do not need to round up, resulting in 0.6931.
Logarithm Base e
The natural logarithm (denoted as 'ln') is the logarithm to the base e. The number e is an irrational constant approximately equal to 2.71828. The natural logarithm of a number x (written as \( \ln x \)) tells us how many times we need to multiply e to get x.
For instance, \( \ln 2 \) asks, 'To what power must e be raised to obtain 2?' By using a calculator, this is found to be approximately 0.6931. Understanding this logarithm helps in many fields, including calculus, complex numbers, and exponential growth analysis.
Mathematical Procedure
Solving mathematical problems efficiently often involves following a well-defined procedure. Here's the procedure we followed to solve for \( \ln 2 \):
  • First, understand what the problem is asking. Here, we need to find the natural logarithm of 2 to four decimal places.
  • Then, use a scientific calculator to perform the calculation. Enter the number 2 and press the 'ln' button.
  • Read the output from the calculator, which is typically displayed with numerous decimal places.
  • Round this result to the required number of decimal places. In our case, we rounded the value to four decimal places, resulting in 0.6931.
  • Finally, write down the answered rounded to four decimal places for documentation.

This methodical approach ensures accuracy and precision in mathematical problem-solving.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify. $$ \log _{81} 3 \cdot \log _{3} 81 $$

Simplify. $$ \log _{1 / 5} 25 $$

Atmospheric pressure \(P\) at altitude \(a\) is given by $$ P(a)=P_{0} e^{-0.00005 a} $$ where \(P_{0}\) is the pressure at sea level \(\approx 14.7 \mathrm{lb} / \mathrm{in}^{2}\) (pounds per square inch). Explain how a barometer, or some other device for measuring atmospheric pressure, can be used to find the height of a skyscraper.

Solve. $$\log _{2} 80+\log _{2} x=5$$

Express as an equivalent expression that is a sum or a difference of logarithms and, if possible, simplify. If \(\log _{a} x=2, \log _{a} y=3,\) and \(\log _{a} z=4,\) what is $$\log _{a} \frac{\sqrt[3]{x^{2} z}}{\sqrt[3]{y^{2} z^{-2}}} ?$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.