/*! 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 39 Use a calculator to evaluate the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 39

Use a calculator to evaluate the expression, correct to four decimal places. $$ \begin{array}{llll}{\text { (a) } \ln 5} & {\text { (b) } \ln 25.3} & {\text { (c) } \ln (1+\sqrt{3})}\end{array} $$

Short Answer

Expert verified
(a) \(\ln 5 \approx 1.6094\); (b) \(\ln 25.3 \approx 3.2317\); (c) \(\ln (1+\sqrt{3}) \approx 1.0040\).

Step by step solution

01

Identify the Expression

We need to evaluate three different expressions involving the natural logarithm (\(\ln\)). These are \(\ln 5\), \(\ln 25.3\), and \(\ln (1+\sqrt{3})\).
02

Calculate \(\ln 5\)

Use a scientific calculator to evaluate \(\ln 5\). Enter 5 on the calculator and press the \(\ln\) function key. The result should be approximately 1.6094.
03

Calculate \(\ln 25.3\)

Enter 25.3 into the calculator and press the \(\ln\) function key to find \(\ln 25.3\). The result should be approximately 3.2317.
04

Calculate \(\ln (1+\sqrt{3})\)

First, calculate \(\sqrt{3}\) on the calculator, which is approximately 1.7321. Then, add 1 to get approximately 2.7321. Now, find the natural logarithm of this sum using the \(\ln\) function key. The result should be approximately 1.0040.

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
A scientific calculator is a powerful tool that helps in evaluating complex mathematical expressions. It is specially designed for calculations involving logarithms, exponentials, powers, and roots. To effectively use a scientific calculator, it's important to familiarize yourself with its buttons and functions. Here's a simple guide on how to use it:
  • Locate the "ln" button for natural logarithms. This button is typically labeled with "ln," and it calculates the natural logarithm of a number.
  • For operations like square roots, look for the square root symbol (鈭�) on the calculator.
  • Remember, you can enter values directly using the number keys followed by the desired operation key (like "ln" or "鈭�").
Using a scientific calculator not only speeds up the calculation process but also ensures accuracy in decimal places, crucial for tasks requiring precision.
Evaluating Expressions
Evaluating mathematical expressions, especially those involving natural logarithms, is an essential skill in algebra and calculus. To evaluate an expression means to find its numerical value using mathematical rules. Here's how you can approach evaluating expressions:
  • Identify the expression you need to evaluate. Make sure to understand each component, such as whether it involves exponentiation, square roots, or other mathematical operations.
  • Use your scientific calculator effectively by entering the components in the correct order. For example, in the expression \(\ln (1+\sqrt{3})\), compute the square root first, then add it to 1, and finally compute the logarithm.
  • Always round your final answer to the required decimal places, which, in this case, is four decimal places for higher precision.
Practicing the evaluation of different types of expressions helps develop a stronger understanding of mathematical concepts and improves problem-solving skills.
Square Root Calculations
Calculating the square root is a fundamental operation that can be easily performed with a scientific calculator. The square root of a number \(x\) is a value that, when multiplied by itself, gives \(x\). Square root calculations are often part of larger expressions as seen in expressions like \(\ln (1+\sqrt{3})\).To perform a square root calculation:
  • Enter the number you need to find the square root of on the calculator.
  • Press the square root button (often depicted as 鈭�) to calculate.
The calculator displays the result, which you can use in further computations, such as adding it to another number or applying a logarithm function. Understanding how to calculate and interpret square roots is indispensable for tackling various types of mathematical 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

Population of a Country The population of a country has a relative growth rate of 3\(\%\) per year. The government is trying to reduce the growth rate to \(2 \% .\) The population in 1995 was approximately 110 million. Find the projected population for the year 2020 for the following conditions. (a) The relative growth rate remains at 3\(\%\) per year. (b) The relative growth rate is reduced to 2\(\%\) per year.

Draw the graph of the function in a suitable viewing rec- tangle, and use it to find the domain, the asymptotes, and the local maximum and minimum values. $$ y=x(\ln x)^{2} $$

Bacteria Culture A culture starts with 8600 bacteria. After one hour the count is \(10,000\) . (a) Find a function that models the number of bacteria \(n(t)\) after \(t\) hours. (b) Find the number of bacteria after 2 hours. (c) After how many hours will the number of bacteria double?

Use a graphing device to find all solutions of the equation, rounded to two decimal places. \(e^{x^{2}}-2=x^{3}-x\)

Difficulty of a Task The difficulty in "acquiring a target" such as using your mouse to click on an icon on your computer screen) depends on the distance to the target and the size of the target. According to Fits's Law, the index of difficulty (ID) is given by $$ \mathrm{ID}=\frac{\log (2 A / W)}{\log 2} $$ where \(W\) is the width of the target and \(A\) is the distance to the center of the target. Compare the difficulty of clicking on an icon that is 5 \(\mathrm{mm}\) wide to clicking on one that is 10 \(\mathrm{mm}\) wide. In each case, assume that the mouse is 100 \(\mathrm{mm}\) from the icon.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.