Using numerical analysis and the Power Rule of Logarithms, how can log(1/343)

Question

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

Answer 1

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).