To rewrite \( \log(1343) \) using numerical analysis and the Power Rule of Logarithms, we first need to consider breaking down the number \( 1343 \) into its prime factors or into a more manageable form.
However, the provided options contain expressions that do not directly relate to the logarithm of \( 1343 \). The Power Rule of Logarithms states that:
\[ \log(a^b) = b \cdot \log(a) \]
Given the options you provided, let's analyze them:
- log−21: This doesn't relate to \( 1343 \).
- 7log−3: This suggests that \( 1343 \) can be expressed as something raised to the power of 7 and involves \( \log(-3) \), which is not relevant.
- −3log7: This implies \( 1343 \) could be expressed related to \( 7^{-3} \), which does not make sense in this context.
- 3log−7: Similarly, this is not a valid representation of \( \log(1343) \).
Since none of the options correctly reflect a logical analytical breakdown of \( \log(1343) \) using numerical analysis or logarithmic properties, it appears there may be a misunderstanding or misapplication of the Power Rule in the options given.
In standard practice, \( \log(1343) \) would generally remain as is unless a specific base is provided or a reformulation through certain factors is required.
Thus, based on the choices and without further context, none of these responses accurately rewrite \( \log(1343) \) using the Power Rule or any specific logarithmic properties in a meaningful way.