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

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 16

Use a calculator to find each of the following to four decimal places. $$\log 100$$

Short Answer

Expert verified
2

Step by step solution

01

- Understand Logarithms

A logarithm answers the question: 'To what exponent must a specific base be raised, to produce a given number?' In this problem, we are using the common logarithm, which has a base of 10.
02

- Set Up the Logarithmic Expression

Using the calculator, we need to find \( \log 100 \). This means we are finding the exponent to which 10 must be raised to result in 100.
03

- Use a Calculator

Enter \( \log 100 \) into the calculator. A scientific calculator will have a 'log' button, which implies base 10. The calculator shows \( \log 100 = 2 \).

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.

common logarithm
Logarithms are mathematical tools used to determine the exponent that a certain base must be raised to, in order to produce a specific number. In this particular case, we are dealing with the common logarithm. This type of logarithm always uses a base of 10.
Common logarithms are widely used in various scientific fields and real-world applications because they simplify calculations with large numbers. For instance, they are very useful in scenarios involving exponential growth or decay, such as population studies and radioactive decay.
base 10
Understanding the base of a logarithm is crucial. The base of a logarithm tells you what number you are repeatedly multiplying to get to your result. With common logarithms, this base is always 10, which is why they are easily calculated using a standard scientific calculator.
Here鈥檚 an essential point to remember: When you see \(\text{log}\) without any specified base, it defaults to base 10. This notation helps save space and avoids repetition. For example, \(\text{log} 100\) automatically means \(\text{log}_{10} 100\).
Practicing with different values can help solidify your understanding. For example:
  • \(\text{log} 10 = 1\) because \(\text{10}^1 = 10\)
  • \(\text{log} 1000 = 3\) because \(\text{10}^3 = 1000\)
  • \(\text{log} 1 = 0\) because \(\text{10}^0 = 1\)
scientific calculator
Using a scientific calculator to find logarithms is straightforward. Most scientific calculators have a dedicated 'log' button. This button is used to find log values for base 10 logarithms.
Here鈥檚 a simple guide to using your calculator for this task:
  • Turn on your scientific calculator.
  • Press the 'log' button. This automatically assumes base 10.
  • Enter the number you want the logarithm of, in this example, 100.
  • Press the 鈥�=鈥� or 鈥楨nter鈥� button to get the result.
Following these steps, if you input \(\text{log} 100\), you should get the output as 2. This means that \(\text{10}^2 = 100\).
Remember to practice with different numbers to get comfortable with using the log function on your calculator.

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. If no solution exists, state this. $$ 3^{2 x}-8 \cdot 3^{x}+15=0 $$

Find a linear function whose graph has the given characteristics. Perpendicular to \(y=\frac{1}{2} x+3 ; y\) -intercept: \((0,8)\)

In 2016 , the population of the United States was 324 million and the exponential growth rate was \(0.73 \%\) per year. Data: U.S. Census Bureau a) Find the exponential growth function. b) Estimate the U.S. population in 2025 c) When will the U.S. population reach 400 million?

Solve. If no solution exists, state this. $$ 3^{x^{2}} \cdot 3^{4 x}=\frac{1}{27} $$

The world population \(P(t),\) in billions, t years after 2010 can be approximated by $$ P(t)=6.9(1.011)^{t} $$ Data: U.S. Census Bureau; International Data Base a) In what year will the world population reach 10 billion? b) Find the doubling time.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Discrete 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.