To evaluate \( \log\left(\frac{10^4}{5}\right) \) using the Power Rule of Logarithms, we first apply the Quotient Rule:
\[ \log\left(\frac{a}{b}\right) = \log(a) - \log(b) \]
So, we can rewrite the logarithm as:
\[ \log\left(\frac{10^4}{5}\right) = \log(10^4) - \log(5) \]
Next, we apply the Power Rule of Logarithms, which states:
\[ \log(a^b) = b \cdot \log(a) \]
Using this rule on \( \log(10^4) \):
\[ \log(10^4) = 4 \cdot \log(10) \]
Since \( \log(10) = 1 \) in base 10, we have:
\[ \log(10^4) = 4 \cdot 1 = 4 \]
Putting it all together, we get:
\[ \log\left(\frac{10^4}{5}\right) = 4 - \log(5) \]
Thus, the rewritten logarithm that uses the Power Rule of Logarithms is:
\[ \log\left(\frac{10^4}{5}\right) = 4 - \log(5) \]