To evaluate \(\log_7(492) + \log_7(7)\), we can use the property of logarithms which states that \(\log_b(m) + \log_b(n) = \log_b(m \cdot n)\).
Applying this property here:
\[ \log_7(492) + \log_7(7) = \log_7(492 \cdot 7) \]
Calculating \(492 \cdot 7\):
\[ 492 \cdot 7 = 3444 \]
Now we have:
\[ \log_7(492) + \log_7(7) = \log_7(3444) \]
Next, we need to determine what power of \(7\) gives \(3444\). However, we can simplify this process. The value of \(\log_7(7)\) is \(1\) since \(7^1 = 7\).
Thus:
\[ \log_7(492) + 1 \]
To compare with the given answers, we can estimate \(\log_7(492)\). Since \(7^2 = 49\) and \(7^3 = 343\), we know that \(7^4 = 2401\) and \(7^5 = 16807\), so \(\log_7(492)\) will be slightly above \(3\) because \(343 < 492 < 2401\).
Since \(\log_7(492) + 1\) is also slightly above \(4\):
- \(\log_7(492) \approx 3\)
- \(\log_7(492) + 1 \approx 4\)
Therefore, the value that correctly evaluates \(\log_7(492) + \log_7(7)\) is:
4.