Open in App
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Chapter 3: Chapter 3

Problem 12

Next question

Given that \(\log 3 \approx 0.4771\) and \(\log 4 \approx\) 0.6021, find the value of each logarithm. $$\log \frac{3}{4}$$

Short Answer

Expert verified
The value of \(\log \frac{3}{4}\) is approximately \(-0.1250\).
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Try Premium for free

Over 22 million students worldwide already upgrade their learning with Vaia!

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Use logarithmic property to rewrite given expression

We can rewrite the given logarithm using the logarithmic property as: $$\log \frac{3}{4} = \log 3 - \log 4$$

Step 2: Substitute the given values

Replace the given approximations for \(\log3\) and \(\log4\) in the expression: $$\log \frac{3}{4} = 0.4771 - 0.6021$$

Step 3: Perform the calculation

Subtract the values of \(\log 3\) and \(\log 4\) to find the value of \(\log \frac{3}{4}\): $$\log \frac{3}{4} \approx -0.1250$$ So, the value of \(\log \frac{3}{4}\) is approximately \(-0.1250\).

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 3

Use logarithms to solve the equation for \(t\). $$\frac{1}{3} e^{-3 t}=0.9$$
Chapter 3

The temperature of a cup of coffee \(t\) min after it is poured is given by $$ T=70+100 e^{-0.0446 t} $$ where \(T\) is measured in degrees Fahrenheit. a. What was the temperature of the coffee when it was poured? b. When will the coffee be cool enough to drink (say, $\left.120^{\circ} \mathrm{F}\right) ?$
Chapter 3

Sketch the graph of the equation. $$y=\log _{1 / 3} x$$
Chapter 3

Write the expression as the logarithm of a single quantity. $$\ln 3+\frac{1}{2} \ln x+\ln y-\frac{1}{3} \ln z$$
Chapter 3

Use the laws of logarithms to expand and simplify the expression. $$\ln \frac{e^{x}}{1+e^{x}}$$
See all solutions

More chapters from the book ‘Applied Mathematics: For the Managerial, Life, and Social Sciences’

See all chapters

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App
Create your free account now
Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Math

Calculus

Read Explanation
Math

Statistics

Read Explanation
Math

Mechanics Maths

Read Explanation
Math

Decision Maths

Read Explanation
Math

Probability and Statistics

Read Explanation
Math

Pure Maths

Read Explanation
View all explanations