Question

Using numerical analysis and the Power Rule of Logarithms, how can log (1/343)
be rewritten?(1 point)
Responses

7 log -3
7 log -3

log -21
log -21

3 log -7
3 log -7

-3 log 7

Answer 1

To rewrite \(\log\left(\frac{1}{343}\right)\) using the properties of logarithms, we can use the Power Rule of Logarithms, which states that \(\log\left(\frac{a}{b}\right) = \log(a) - \log(b)\) and also the property that \(\log\left(a^{-1}\right) = -\log(a)\).

First, we note that \(343 = 7^3\). Thus, we can rewrite \(1/343\) as follows:

\[
\frac{1}{343} = \frac{1}{7^3} = 7^{-3}
\]

Now we can express the logarithm:

\[
\log\left(\frac{1}{343}\right) = \log(7^{-3})
\]

Using the Power Rule of Logarithms, we have:

\[
\log(7^{-3}) = -3 \log(7)
\]

Therefore, the expression \(\log(1/343)\) can be rewritten as:

\[
-3 \log(7)
\]

So, the correct response from your options is:

**-3 log 7**