Question
Using numerical analysis and the Power Rule of Logarithms, how can log(
343
1
) be rewritten?
A. 7log−3
B. 3log−7
C. −3log7
D. log−21
343
1
) be rewritten?
A. 7log−3
B. 3log−7
C. −3log7
D. log−21
Answers
Answered by
GPT-4o mini
To rewrite \( \log(343) \) using numerical analysis and the Power Rule of Logarithms, we first note that \( 343 = 7^3 \).
Now we can apply the Power Rule of Logarithms, which states that \( \log(a^b) = b \cdot \log(a) \).
Using this rule, we can write:
\[
\log(343) = \log(7^3) = 3 \cdot \log(7)
\]
This means we can express \( \log(343) \) in terms of \( \log(7) \):
\[
\log(343) = 3\log(7)
\]
This matches none of the provided options exactly, but we want to determine if we can find a match with the negative sign factored into the results.
Looking at the provided answers:
A. \( 7\log(-3) \)
B. \( 3\log(-7) \)
C. \( -3\log(7) \)
D. \( \log(-21) \)
None of these options directly match \( 3\log(7) \), but it seems option C could be interpreted to relate to the change in the sign.
Given all of this and not matching any perfectly since none of the forms would be a substitution or simplified correctly from \( \log(343) \) = \( 3 \log(7) \), if negative values would interchange and reveled a change in its log values, it would be reflected as \( -3\log(7) \).
However, it's crucial to recognize that typically, one would expect \( 3 \log(7) \) itself without any adjustments. Given the provided options and considering common discretion in logarithm properties, the closest adjusted format to keep in alignment scientifically would veer into recognizing:
The answer is **None**, but the choice that realigns with a reciprocal conceptualization lean is:
**C. -3log7**.
Now we can apply the Power Rule of Logarithms, which states that \( \log(a^b) = b \cdot \log(a) \).
Using this rule, we can write:
\[
\log(343) = \log(7^3) = 3 \cdot \log(7)
\]
This means we can express \( \log(343) \) in terms of \( \log(7) \):
\[
\log(343) = 3\log(7)
\]
This matches none of the provided options exactly, but we want to determine if we can find a match with the negative sign factored into the results.
Looking at the provided answers:
A. \( 7\log(-3) \)
B. \( 3\log(-7) \)
C. \( -3\log(7) \)
D. \( \log(-21) \)
None of these options directly match \( 3\log(7) \), but it seems option C could be interpreted to relate to the change in the sign.
Given all of this and not matching any perfectly since none of the forms would be a substitution or simplified correctly from \( \log(343) \) = \( 3 \log(7) \), if negative values would interchange and reveled a change in its log values, it would be reflected as \( -3\log(7) \).
However, it's crucial to recognize that typically, one would expect \( 3 \log(7) \) itself without any adjustments. Given the provided options and considering common discretion in logarithm properties, the closest adjusted format to keep in alignment scientifically would veer into recognizing:
The answer is **None**, but the choice that realigns with a reciprocal conceptualization lean is:
**C. -3log7**.