To evaluate \(\log(104 \cdot 103)\), we can use the logarithmic property that states:
\[ \log(a \cdot b) = \log a + \log b \]
So we can write:
\[ \log(104 \cdot 103) = \log(104) + \log(103) \]
Now, we can express \(104\) and \(103\) in terms of base 10 logarithms:
Let:
- \( \log(104) = \log(10^4) + \log(1.04) = 4 + \log(1.04) \)
- \( \log(103) = \log(10^3) + \log(1.03) = 3 + \log(1.03) \)
But rather, we can directly assume:
\[ \log(104) = 2 \log(10) + \log(4) \text{ and } \log(103) = 2\log(10) + \log(3) \]
However, given the properties of logarithms, the evaluation maintains the base in mind, hence:
\[ \log(104) = 4 + \log(3) \text{ and } \log(103) = 3 + \log(4) \]
Now, adding these gives a total of \(7\) plus any logarithmic offsets for \(4\) or \(3\).
Since \( \log(104 \cdot 103) \) will ultimately yield a direct evaluation to \(7\) under standard bases without significant imports of \(log(1.03)\) or \(log(1.04)\) retaining values within usual metric bases.
Thus, the correct final response here evaluates to:
\[ \boxed{7} \]