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Chapter 5: Problem 58

Find the following using a calculator. Round to four decimal places. $$\log 93,100$$

Short Answer

Expert verified
\(\text{log}_{10} 93100 = 4.9681\)

Step by step solution

01

Understand the Logarithm

The logarithm \(\text{log}_{10} 93100\) represents the power to which the base 10 must be raised to obtain the number 93100. This can be evaluated using a scientific calculator.
02

Enter the Number Into the Calculator

Turn on the scientific calculator. Ensure it is set to the correct mode for evaluating logarithms. Enter the number 93100.
03

Calculate the Logarithm

Now, press the \(\text{log}\) button on the calculator. This will calculate the common logarithm of 93100.
04

Round the Result

The calculator will provide a result. Round this result to four decimal places. The answer should be displayed as a four-decimal number.

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Key Concepts

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

Common Logarithm
In mathematics, a common logarithm is a logarithm with base 10. We usually write it as \(\text{log}_{10} x\). This function tells us what power we need to raise 10 to get the number x. For example, if we have \(\text{log}_{10} 100\), we know that 10 must be raised to the power of 2 to get 100, so \(\text{log}_{10} 100 = 2\).
Scientific Calculator
A scientific calculator is an essential tool in mathematics for functions beyond simple arithmetic, such as trigonometry, logarithms, and exponential functions. To calculate the common logarithm of a number with a scientific calculator, follow these steps:
  • Turn on the calculator.
  • Ensure it鈥檚 set to the correct mode, typically the 'log' mode for common logarithms.
  • Enter the number you want to find the logarithm for, in this case, 93100.
  • Press the \(\text{log}\) button to get the result.
This will give you the common logarithm of the entered number. These calculated values aid in various scientific and mathematical computations.
Rounding Numbers
Rounding numbers is a fundamental skill in mathematics, ensuring values are simplified while maintaining a level of precision. When rounding to four decimal places, you follow a straightforward process:
  • Identify the fifth decimal place.
  • If the fifth digit is 5 or higher, round the fourth place up by one.
  • If the fifth digit is less than 5, retain the current value of the fourth place.
For the logarithm of 93100, after calculating with a scientific calculator, you might get a long result. For example, if the calculator shows 4.968482948, you would round to 4.9685, as the fifth digit (8) is greater than 5.

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Most popular questions from this chapter

U.S. Imports. The amount of imports to the United States has increased exponentially since 1980 (Sources: U.S. Census Bureau; U.S. Bureau of Economic Analysis; U.S. Department of Commerce). The exponential function $$ I(x)=297.539(1.075)^{x} $$ where \(x\) is the number of years after \(1980,\) can be used to estimate the total amount of U.S. imports, in billions of dollars. Find the total amount of imports to the United States in \(1995,\) in \(2005,\) in \(2010,\) and in \(2013 .\) Round to the nearest billion dollars. (IMAGE CANT COPY)

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