Answer :
To determine which option is equivalent to the expression [tex]\(\log 4 - \log 24\)[/tex], we can use the properties of logarithms. Specifically, one of the properties we can use is:
[tex]\[ \log a - \log b = \log \left( \frac{a}{b} \right) \][/tex]
### Step-by-Step Solution:
1. Apply the property of logarithms:
[tex]\[ \log 4 - \log 24 = \log \left( \frac{4}{24} \right) \][/tex]
2. Simplify the fraction inside the logarithm:
[tex]\[ \frac{4}{24} = \frac{1}{6} \][/tex]
3. Rewrite the logarithmic expression:
[tex]\[ \log \left( \frac{1}{6} \right) \][/tex]
### Conclusion:
The expression [tex]\(\log 4 - \log 24\)[/tex] simplifies to [tex]\(\log \left( \frac{1}{6} \right)\)[/tex].
Therefore, the correct answer is:
C. [tex]\(\log \left( \frac{1}{6} \right)\)[/tex]
[tex]\[ \log a - \log b = \log \left( \frac{a}{b} \right) \][/tex]
### Step-by-Step Solution:
1. Apply the property of logarithms:
[tex]\[ \log 4 - \log 24 = \log \left( \frac{4}{24} \right) \][/tex]
2. Simplify the fraction inside the logarithm:
[tex]\[ \frac{4}{24} = \frac{1}{6} \][/tex]
3. Rewrite the logarithmic expression:
[tex]\[ \log \left( \frac{1}{6} \right) \][/tex]
### Conclusion:
The expression [tex]\(\log 4 - \log 24\)[/tex] simplifies to [tex]\(\log \left( \frac{1}{6} \right)\)[/tex].
Therefore, the correct answer is:
C. [tex]\(\log \left( \frac{1}{6} \right)\)[/tex]
