Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
I need to find the number in the block
![The equation shown is:
\[ 2\log_6 3 = \log_6 \square \]
Here, we are using logarithms with base 6. The expression on the left shows \(2\) times the logarithm of 3 to the base 6. The equation is asking to find the value inside the blank on the right side such that the logarithms are equal.
To solve it, you use properties of logarithms:
- Use the power rule of logarithms: \( a\log_b c = \log_b c^a \).
Applying this here gives:
\[ 2\log_6 3 = \log_6 (3^2) = \log_6 9 \]
Thus, the equation becomes:
\[ \log_6 9 = \log_6 \square \]
Therefore, the value inside the square should be \(9\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a578803-91b9-40e4-b05f-bb33971732bd%2F7aa34b17-151c-4db5-99d2-6eb93a6449aa%2F2ivq82_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The equation shown is:
\[ 2\log_6 3 = \log_6 \square \]
Here, we are using logarithms with base 6. The expression on the left shows \(2\) times the logarithm of 3 to the base 6. The equation is asking to find the value inside the blank on the right side such that the logarithms are equal.
To solve it, you use properties of logarithms:
- Use the power rule of logarithms: \( a\log_b c = \log_b c^a \).
Applying this here gives:
\[ 2\log_6 3 = \log_6 (3^2) = \log_6 9 \]
Thus, the equation becomes:
\[ \log_6 9 = \log_6 \square \]
Therefore, the value inside the square should be \(9\).
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