/*! 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 16 Find logarithm. Give approximati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 16

Find logarithm. Give approximations to four decimal places. \(\ln 8.32\)

Short Answer

Expert verified
\(\ln 8.32 \approx 2.1199\)

Step by step solution

01

- Understand the Problem

We need to find the natural logarithm (ln) of 8.32 and provide an approximation to four decimal places.
02

- Use a Calculator

Input the value 8.32 into a scientific calculator and press the ln button to find the natural logarithm.
03

- Note the Result

The calculator shows that \(\ln 8.32 \) is approximately 2.1199.

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.

logarithm calculation
To start, let's break down what a logarithm is, particularly the natural logarithm ( \( \ln \) ). A logarithm helps in finding out the power to which a base number must be raised to get another number. For instance, if you have \( 10^2 = 100 \), the base 10 logarithm of 100 is 2, written as \( \log_{10}(100) = 2 \). A natural logarithm uses the base e, which is approximately 2.71828. So, \( \ln(x) \) means the power you need to raise e to get x. In this exercise, we need to find \( \ln(8.32) \). By understanding this, you can use logarithms to solve numerous real-world problems involving exponential growth or decay.
scientific calculator
Using a scientific calculator can significantly simplify finding logarithmic values. These calculators have a dedicated button for natural logarithms, usually labeled as 'ln'. Here's how to use it:
  • Turn on the calculator.
  • Enter the value for which you want to find the natural logarithm (in this case, 8.32).
  • Press the 'ln' button.
  • The calculator will display the natural logarithm of 8.32, which, for our case, is approximately 2.1199.
Using these steps, you can quickly find logarithmic values for any decimal or integer. This makes solving problems much faster and more accurate.
decimal approximation
When dealing with logarithms, especially in scientific and mathematical contexts, it鈥檚 often necessary to approximate values to a certain number of decimal places. In this exercise, we approximated \( \ln(8.32) \) to four decimal places. Here鈥檚 how you can do it:
  • After obtaining the logarithmic value using a scientific calculator, look at the number displayed, usually having several decimal digits.
  • Identify the first four digits after the decimal point. For our example, \( 2.119905 \) becomes 2.1199 when approximated to four decimal places.
  • If the fifth digit is 5 or more, round the fourth digit up by one. If it鈥檚 less than 5, keep the fourth digit as it is.
This method helps in achieving precision, which is crucial in both academic and practical applications. It also ensures that students develop accuracy in their mathematical calculations.

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

If \(f(x)=4^{x},\) find value indicated. Use a calculator, and give the answer to the nearest hundredth. \(f(2.73)\)

For \(1981-2003,\) the number of billion cubic feet of natural gas gross withdrawals from crude oil wells in the United States can be approximated by the function defined by $$f(x)=3800+585 \log _{2} x$$ where \(x=1\) represents \(1981, x=2\) represents \(1982,\) and so on. (Source: Energy Information Administration.) Use this function to approximate the number of cubic feet withdrawn in \(2003,\) to the nearest unit.

Which point lies on the graph of \(f(x)=3^{x} ?\) A. \((1,0)\) B. \((3,1)\) C. \((0,1)\) D. \(\left(\sqrt{3}, \frac{1}{3}\right)\)

Find each logarithm. Give approximations to four decimal places. \(\ln 10\)

Solve equation. \(\log _{1 / 2} 8=x\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.