To evaluate \( \log(104 \cdot 103) \), you can use the property of logarithms that states:
\[ \log(a \cdot b) = \log(a) + \log(b) \]
Applying this property:
\[ \log(104 \cdot 103) = \log(104) + \log(103) \]
Now we can simplify each term.
The logarithm of a number can be expressed in a different base if we need to use common logarithm properties or simplifications, but right now, no specific base is given. Assuming the logarithm is in base 10:
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Break down \( 104 \) and \( 103 \) if necessary, but in this context, they can be left as is, since \( \log(104) \) and \( \log(103) \) do not simplify further in a basic way.
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Add the two terms \( \log(104) + \log(103) \).
If you have access to a calculator or logarithm tables, you can compute these values, but typically you don't have exact simple logarithmic expressions for \( 104 \) and \( 103 \).
Therefore, since \( 10^2 = 100 \) and \( 10^3 = 1000 \), it's apparent that \( 104 \) and \( 103 \) are both between 100 and 1000.
To approximate without a calculator:
- \( \log(100) = 2 \)
- \( \log(1000) = 3 \) Thus, you can expect \( \log(104) \) to be slightly greater than \( 2 \) and \( \log(103) \) to be slightly greater than \( 2 \).
Overall, there is no direct answer here without numeric approximations, but you can evaluate: \[ \log(104) + \log(103) \]
If you need an exact numerical response, please specify the base or let me know if you would like to use approximations.
Given your multiple choice options for the evaluation, it seems you're looking for a precise answer. Since you suggested \( 4 + \log 3 \), \( \log 4 + 3 \), \( 7 \), and \( 12 \), it might be that I misunderstood your expression. However, none of them likely matches \( \log(104 \cdot 103) \) without further elaboration about your mathematical context or the specific logarithmic values.
Let me know how you'd like to proceed!