/*! 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 25 Use a calculator to find each of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 25

Use a calculator to find each of the following to four decimal places. $$ \ln 9 $$

Short Answer

Expert verified
\(\ln 9 \approx 2.1972\)

Step by step solution

01

Understand the problem

The task is to find the natural logarithm of 9, denoted as \(\backslash ln 9\), and round the result to four decimal places using a calculator.
02

Locate the natural logarithm function on the calculator

Find the \( \backslash ln \) button on the scientific calculator. It might be a separate button or accessed by pressing a 'shift' or '2nd' key before another button.
03

Input the value and calculate

Press the \( \backslash ln \) button, then enter the number 9. Press the '=' or 'Enter' key to compute the natural logarithm of 9.
04

Record the result

Read the result from the calculator display and round it to four decimal places if necessary. The result should be approximately 2.1972.

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.

natural logarithm
The natural logarithm, often denoted as \(\backslash ln\), is a fundamental function in mathematics that is the inverse of the exponential function \(e^x\). It specifically calculates the power to which the base \(e\) (approximately 2.71828) must be raised to obtain a given number.
For example, \( \backslash ln (e) = 1\) because \(e^1 = e\).
In simpler terms, \( \backslash ln 9\) asks the question: 'To what power must \(e\) be raised to get 9?'. This type of logarithm is widespread in various fields like economics, biology, and physics due to its natural growth and decay properties.
calculator usage
Using a calculator to find the natural logarithm is straightforward once you know where to find the function. Most scientific calculators have a dedicated \( \backslash ln \) button:
  • First, ensure your calculator is switched on and set to the correct mode (degrees/radians are not usually relevant here).
  • Locate the \( \backslash ln \) button鈥攖his might be a standalone button or require pressing a 'shift' or '2nd' key first.
  • Press the \( \backslash ln \) button and enter the value for which you want to find the natural logarithm (in this case, 9).
  • Press '=' or 'Enter' to calculate.

Once done, your calculator will display the natural logarithm of the number you entered. Always verify the mode and button to get accurate results.
rounding numbers
Rounding numbers is an essential skill to ensure results are practical for real-world applications and comparisons. When rounding to four decimal places, follow these rules:
  • Identify the fourth decimal place.
  • Look at the fifth decimal place to decide whether to round up or stay the same. If the fifth digit is 5 or higher, increase the fourth digit by one. Otherwise, leave it.
  • In the given example, if your calculator shows 2.197224577, you note the first four decimal digits (1972) and the fifth digit (2). Since 2 is less than 5, the final result remains 2.1972.

This way, you ensure your answers comply with the precision needed for specific problems.

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

Solve for \(x\). Give an approximation to four decimal places. $$ \log 692+\log x=\log 3450 $$

Solve. If no solution exists, state this. $$ \left(81^{x-2}\right)\left(27^{x+1}\right)=9^{2 x-3} $$

Atmospheric pressure \(P\) at an elevation \(a\) feet above sea level can be estimated by $$ P=P_{0} e^{-0.00004 a} $$ where \(P_{0}\) is the pressure at sea level, which is approximately 29.9 in. of mercury (Hg). Explain how a barometer, or some other device for measuring atmospheric pressure, can be used to find the height of a skyscraper.

Find each of the following, given that $$f(x)=\frac{1}{x+2} \quad \text { and } \quad g(x)=5 x-8$$$$(g-f)(x)$$

The function \(V(t)=750(1.2)^{t}\) is used to predict the value \(V(t)\) of a certain rare stamp \(t\) years after \(2016 .\) Do not calculate \(V^{-1}(t),\) but explain how \(V^{-1}\) could be used.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.