[tex]log _6 36+log _3 27=[/tex]
Answer (1)
Evaluate lo g 6 36 : Since 6 2 = 36 , lo g 6 36 = 2 .
Evaluate lo g 3 27 : Since 3 3 = 27 , lo g 3 27 = 3 .
Add the two results: 2 + 3 = 5 .
The final answer is 5 .
Explanation
Understanding the problem We are given the expression lo g 6 36 + lo g 3 27 = . We need to evaluate this expression.
Evaluating the first logarithm Let's evaluate lo g 6 36 . We need to find the power to which we must raise 6 to get 36. Since 6 2 = 36 , we have lo g 6 36 = 2 .
Evaluating the second logarithm Now, let's evaluate lo g 3 27 . We need to find the power to which we must raise 3 to get 27. Since 3 3 = 27 , we have lo g 3 27 = 3 .
Adding the results Finally, we add the two results: 2 + 3 = 5 .
Final Answer Therefore, lo g 6 36 + lo g 3 27 = 2 + 3 = 5 . The correct answer is A.
Examples
Logarithms are used in many real-world applications, such as measuring the intensity of earthquakes (the Richter scale), the loudness of sounds (decibels), and the acidity of a solution (pH). Understanding logarithms helps us to quantify and compare these phenomena. For example, an earthquake with a magnitude of 6 on the Richter scale is ten times more intense than an earthquake with a magnitude of 5.
