Use a calculator to find the common logarithm. [tex]$\log 3$[/tex]
Select the correct choice below and fill in any answer boxes within your choice.
A. The answer is [tex]$\square$[/tex]. (Round to four decimal places.)
B. The solution does not exist.
Answer (2)
Find the common logarithm of 3 using a calculator.
Round the result to four decimal places.
The common logarithm of 3 rounded to four decimal places is 0.4771.
The final answer is 0.4771 .
Explanation
Understanding the problem We are asked to find the common logarithm of 3, which is denoted as lo g 3 or lo g 10 3 . This means we need to find the power to which we must raise 10 to get 3.
Calculating the logarithm Using a calculator, we find that the common logarithm of 3 is approximately 0.4771212547.
Rounding the result We are asked to round the answer to four decimal places. Looking at the fifth decimal place, which is 2, we don't need to round up. Therefore, the common logarithm of 3 rounded to four decimal places is 0.4771.
Final Answer The answer is 0.4771.
Examples
Logarithms are used in many real-world applications, such as measuring the intensity of earthquakes (Richter scale), the loudness of sound (decibels), and the acidity or alkalinity of a solution (pH scale). For example, the Richter scale uses logarithms to quantify the size of an earthquake. An earthquake of magnitude 6 is ten times stronger than an earthquake of magnitude 5. Understanding logarithms helps us interpret these scales and make informed decisions based on the data. Logarithmic scales are also used in finance to calculate returns on investments and in computer science to analyze the efficiency of algorithms.
The common logarithm of 3 is calculated using a calculator, yielding approximately 0.4771212547. When rounded to four decimal places, the result is 0.4771. Therefore, the answer is 0.4771.
;
