To solve the expression \( \log_7 492 + \log_7 7 \), we can use the property of logarithms that states:
\[ \log_b a + \log_b c = \log_b (a \cdot c) \]
Applying this property, we have:
\[ \log_7 492 + \log_7 7 = \log_7 (492 \cdot 7) \]
Next, we calculate \( 492 \cdot 7 \):
\[ 492 \cdot 7 = 3444 \]
Now we rewrite the expression:
\[ \log_7 (492 \cdot 7) = \log_7 3444 \]
To find the value of \( \log_7 3444 \), we need to express 3444 as a power of 7 or approximate it using logarithm values. However, since the options provided are whole numbers, we will evaluate \( 7^3 \) and \( 7^4 \) to see where 3444 falls.
Calculating powers of 7:
- \( 7^3 = 343 \)
- \( 7^4 = 2401 \)
- \( 7^5 = 16807 \)
Thus, \( 7^3 < 3444 < 7^5 \). This indicates that \( \log_7 3444 \) is between 4 and 5.
However, upon calculating \( 3444 / 7 \):
\[ 3444 \div 7 = 492 \]
The logarithmic calculation may not yield an integer, but seeing as input choices are finite integers, and knowing approximate calculations or logarithmic properties, we can make an informed choice.
Given the choices are:
- 3
- 4
- 5
- 6
Since \( 3444 \) is quite larger than \( 2401 \) and less than \( 16807 \), we deduce:
- \( \log_7 3444 \) should approximate towards 5, making it the most reasonable assumption given the context of scaling and that it's the closest bound.
Thus, the best value that evaluates \( \log_7 492 + \log_7 7 \) is:
\[ \boxed{5} \]