/*! 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 8 In \(3-14,\) find the common log... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 8

In \(3-14,\) find the common logarithm of each number to the nearest hundredth. $$ 5,620 $$

Short Answer

Expert verified
The common logarithm of 5,620 is approximately 3.75.

Step by step solution

01

Understanding the Problem

We need to find the common logarithm (logarithm to the base 10) of the number 5,620 and round it to the nearest hundredth.
02

Calculate the Common Logarithm

Use a calculator to find the common logarithm of 5,620. Input the number into the calculator and press the 'log' function. This gives us the value of \( \log_{10}(5620) \).
03

Approximate the Result

The result from the calculator is approximately 3.74967. We need to round this to the nearest hundredth.
04

Round to the Nearest Hundredth

To round 3.74967 to the nearest hundredth, look at the third decimal place (the thousandths place). Since it's more than 5, increase the second decimal place by one. Thus, 3.74967 rounds to 3.75.

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 Base 10
A common logarithm is simply a logarithm that has a base of 10. It's very handy for simplifying calculations with large numbers. The notation generally used is \( \log_{10} \) or just \( \log \) if the base is understood to be 10.
  • The expression \( \log_{10}(x) \) asks: "To what power must 10 be raised, to equal \( x \)?"
  • For example, \( \log_{10}(100) = 2 \) because \( 10^2 = 100 \).

Calculating the common logarithm of a number like 5,620 involves discovering the exponent that makes 10 raised to that power equal to 5,620. Using a calculator can help to quickly find results for complex numbers.
Rounding Decimals
Rounding decimals can be made simple with consistent practice. When rounding, you often focus on a particular decimal place. For example, rounding to the nearest hundredth means you look at the thousandths digit to decide.
  • If the digit in the thousandths place is 5 or more, you round up the hundredths digit.
  • If it's less than 5, you simply leave the hundredths digit as it is.
Take the number 3.74967: the digit 9 is in the hundredths place. The digit 6 is in the thousandths place, which is more than 5. Hence, you round the 9 up to 10. This effectively increases the digit in the tenths place by 1 due to carrying over, making the rounded number 3.75. Remember, rounding makes numbers easier to work with while retaining as much of their true value as necessary.
Using a Calculator
Using a calculator efficiently is a great skill, especially when working with functions like common logarithms. Modern calculators have specific buttons for logarithms, commonly labeled as 'log'.

Here's a simple guide:
  • To find the logarithm of a number like 5,620, enter the number into the calculator.
  • Press the 'log' button to see the result.
Most scientific calculators will handle this for you without extra input, providing you instantaneous results. For the common logarithm of 5,620, a calculator will directly give you a long decimal, but it helps you in rounding it to the desired decimal place for precision.

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

The decay constant of francium is \(-0.0315\) minutes. a. After how many minutes will 1.25 grams of francium remain of a 10.0 -gram sample? Assume the exponential decay occurs continuously. b. What is the half-life of francium? (The half-life of an element is the length of time needed for half of a sample to decay. For example, it is the length of time for a sample of 10 grams to be reduced to 5 grams of the original element.)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln \frac{1}{3} $$

Write the following expression as a multiple, sum, and/or difference of logarithms: \(\log \sqrt{\frac{x y}{z}}\)

In \(33-44,\) if \(\ln 2=x\) and \(\ln 3=y,\) write each of the natural logs in terms of \(x\) and \(y\) $$ \ln \frac{1}{2} $$

In \(3-14,\) find the natural logarithm of each number to the nearest hundredth. $$ 8.56 $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

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.