The correct response to the question about the first step in establishing that \( \log(10^7 \cdot 5) = 7 + \log(5) \) is:
The first step is to rewrite the expression using addition, such that \( \log(10^7 \cdot 5) = \log(10^7) + \log(5) \).
This step utilizes the Product Rule of Logarithms, which states that the logarithm of a product is equal to the sum of the logarithms of the factors. Here, you recognize that you can break down \( \log(10^7 \cdot 5) \) into \( \log(10^7) \) and \( \log(5) \). Since \( \log(10^7) \) equals \( 7 \), it follows that the equation simplifies to \( 7 + \log(5) \).