Asked by d
Using numerical analysis and the Power Rule of Logarithms, how can log(1/343)
be rewritten?(1 point)
Responses
−3 log7
negative 3 logarithm 7
log−21
logarithm negative 21
3 log−7
3 logarithm negative 7
7 log−3
be rewritten?(1 point)
Responses
−3 log7
negative 3 logarithm 7
log−21
logarithm negative 21
3 log−7
3 logarithm negative 7
7 log−3
Answers
Answered by
GPT-4o mini
To rewrite \( \log(1/343) \) using the Power Rule of Logarithms and other properties, we can follow these steps:
1. Recognize that \( 343 = 7^3 \). This gives us \( \frac{1}{343} = 7^{-3} \).
2. Rewrite the logarithm:
\[
\log\left(\frac{1}{343}\right) = \log(7^{-3}).
\]
3. Apply the Power Rule of Logarithms, which states that \( \log(a^b) = b \cdot \log(a) \):
\[
\log(7^{-3}) = -3 \log(7).
\]
Thus, \( \log(1/343) \) can be rewritten as \( -3 \log(7) \).
The correct response is: **−3 log7** (negative 3 logarithm 7).
1. Recognize that \( 343 = 7^3 \). This gives us \( \frac{1}{343} = 7^{-3} \).
2. Rewrite the logarithm:
\[
\log\left(\frac{1}{343}\right) = \log(7^{-3}).
\]
3. Apply the Power Rule of Logarithms, which states that \( \log(a^b) = b \cdot \log(a) \):
\[
\log(7^{-3}) = -3 \log(7).
\]
Thus, \( \log(1/343) \) can be rewritten as \( -3 \log(7) \).
The correct response is: **−3 log7** (negative 3 logarithm 7).