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Answer :
To find which expression is equivalent to [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex], we'll simplify step-by-step using properties of logarithms.
1. Understand the Problem:
We have the expression [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex]. We need to determine which logarithmic expression it equals from the given options.
2. Properties of Logarithms:
- The change of base formula tells us that [tex]\(\frac{\log_b a}{\log_b c} = \log_c a\)[/tex].
3. Apply the Formula:
Applying the change of base formula to [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex], we get:
[tex]\[
\log_{16} 128
\][/tex]
4. Conclusion:
Therefore, the expression equivalent to [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex] is [tex]\(\log_{16} 128\)[/tex].
The correct answer is [tex]\(\log_{16} 128\)[/tex].
1. Understand the Problem:
We have the expression [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex]. We need to determine which logarithmic expression it equals from the given options.
2. Properties of Logarithms:
- The change of base formula tells us that [tex]\(\frac{\log_b a}{\log_b c} = \log_c a\)[/tex].
3. Apply the Formula:
Applying the change of base formula to [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex], we get:
[tex]\[
\log_{16} 128
\][/tex]
4. Conclusion:
Therefore, the expression equivalent to [tex]\(\frac{\log_2 128}{\log_2 16}\)[/tex] is [tex]\(\log_{16} 128\)[/tex].
The correct answer is [tex]\(\log_{16} 128\)[/tex].
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