We appreciate your visit to Identify the expression equivalent to tex frac log 2 128 log 2 16 tex A tex log 128 16 tex B tex log 4 128. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve the problem of identifying an equivalent expression to [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex], we can simplify and evaluate this expression using logarithmic properties. Here's how you can do it:
1. Evaluate the Numerator and Denominator:
- [tex]\(\log_2 128\)[/tex]: Since [tex]\(128 = 2^7\)[/tex], we know that [tex]\(\log_2 128 = 7\)[/tex].
- [tex]\(\log_2 16\)[/tex]: Since [tex]\(16 = 2^4\)[/tex], we know that [tex]\(\log_2 16 = 4\)[/tex].
2. Simplify the Expression:
- Now, replace the logs with their values: [tex]\(\frac{\log_2 128}{\log_2 16} = \frac{7}{4}\)[/tex].
3. Expression in Terms of Another Logarithm:
- By the change of base formula, [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex] simplifies to [tex]\(\log_{16} 128\)[/tex].
4. Final Answer:
- Therefore, the expression equivalent to [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex] is [tex]\(\log_{16} 128\)[/tex].
In summary, [tex]\(\log_{16} 128\)[/tex] is the correct answer.
1. Evaluate the Numerator and Denominator:
- [tex]\(\log_2 128\)[/tex]: Since [tex]\(128 = 2^7\)[/tex], we know that [tex]\(\log_2 128 = 7\)[/tex].
- [tex]\(\log_2 16\)[/tex]: Since [tex]\(16 = 2^4\)[/tex], we know that [tex]\(\log_2 16 = 4\)[/tex].
2. Simplify the Expression:
- Now, replace the logs with their values: [tex]\(\frac{\log_2 128}{\log_2 16} = \frac{7}{4}\)[/tex].
3. Expression in Terms of Another Logarithm:
- By the change of base formula, [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex] simplifies to [tex]\(\log_{16} 128\)[/tex].
4. Final Answer:
- Therefore, the expression equivalent to [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex] is [tex]\(\log_{16} 128\)[/tex].
In summary, [tex]\(\log_{16} 128\)[/tex] is the correct answer.
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