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).