To evaluate \( \log(104 \cdot 103) \), we can use the product property of logarithms, which states that \( \log(a \cdot b) = \log(a) + \log(b) \).
So, we can rewrite the expression as follows:
\[ \log(104 \cdot 103) = \log(104) + \log(103) \]
Now we can simplify \( 104 \) as \( 10^4 \) and \( 103 \) as \( 10^3 \):
\[ \log(104) = \log(10^4) = 4 \quad \text{(since \( \log(10^n) = n \))} \] \[ \log(103) = \log(10^3) = 3 \]
Adding these together gives:
\[ \log(104 \cdot 103) = 4 + 3 = 7 \]
Thus, the answer is:
7
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