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Chapter 5: Problem 55

Find the following using a calculator. Round to four decimal places. $$\log 3$$

Short Answer

Expert verified
0.4771

Step by step solution

01

Understand the Problem

The task is to find the logarithm of 3, written as \( \log 3 \), and round the answer to four decimal places.
02

Use a Calculator

Enter 3 into the calculator and find the logarithm function, which is usually labeled as 'log'.
03

Read the Calculator Display

After pressing the log button, the calculator will display the value of \( \log 3 \). This value is approximately 0.4771212547.
04

Round the Answer

Round the value obtained in Step 3 to four decimal places. 0.4771212547 rounds to 0.4771.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calculators
Calculators are essential tools for solving mathematical problems quickly and accurately. When dealing with logarithms, most scientific calculators have a dedicated 'log' button. To find \( \log 3 \), follow these simple steps:
  • Turn on your calculator
  • Enter the number 3
  • Press the 'log' button
The calculator will then display the logarithmic value. This is helpful because calculating logarithms by hand involves complex mathematics. By using a calculator, you can avoid these steps and focus on interpreting the results instead.
Rounding Numbers
Rounding numbers is a technique used to simplify figures, making them easier to work with. To round a number to four decimal places, you need to look at the fifth decimal place. Here is how you do it:
  • If the fifth decimal place is 5 or higher, you round up the fourth decimal place by one.
  • If the fifth decimal place is 4 or lower, you leave the fourth decimal place as is.
For example, the logarithmic value of 3 is approximately 0.4771212547. To round it to four decimal places, we look at the fifth decimal place (2), which is less than 5. Therefore, 0.4771212547 rounds to 0.4771.
Four Decimal Places
Working with numbers to four decimal places provides a good balance between precision and simplicity. In scientific and financial calculations, it's common to round numbers to four decimal places to ensure clarity without losing significant accuracy. When you round \( \log 3 \), you get 0.4771, which is precise enough for most practical purposes. This level of precision is often sufficient for homework, exams, and even some professional applications. Remember, practicing rounding helps build confidence in handling more complex mathematics later on.

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Most popular questions from this chapter

Find the \(x\) -intercepts and the zeros of the function. $$f(x)=2 x^{2}-13 x-7[3.2]$$

Use a graphing calculator to find the point \((s)\) of intersection of the graphs of each of the following pairs of equations. $$y=\left|1-3^{x}\right|, y=4+3^{-x^{2}}$$

Prove each of the following for any base a and any positive number \(x\). $$\log _{a}\left(\frac{x+\sqrt{x^{2}-5}}{5}\right)=-\log _{a}(x-\sqrt{x^{2}-5})$$

Use a graphing calculator to find the approximate solutions of the equation. $$2^{x}-5=3 x+1$$

Determine whether each of the following is true or false. Assume that \(a, x, M,\) and \(N\) are positive. $$\frac{\log _{a} M}{x}=\log _{a} M^{1 / x}$$
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