1. The problem asks to expand the logarithm $\log_2 5x$. 2. Recall the logarithm product rule: $\log_b (MN) = \log_b M + \log_b N$. 3. Applying this rule to $\log_2 5x$, we get: $$\log_2 5x = \log_2 5 + \log_2 x$$ 4. Now, let's check the given options: - $\log_2 5 + \log_2 x$ matches our expansion. - $\log_5 2 + \log_x 2$ is incorrect because the bases and arguments are swapped. - $2\log 5 + 2\log x$ is incorrect because it multiplies the logs by 2 without justification. - $\log_2 5 - \log_2 x$ is incorrect because it subtracts instead of adding. 5. Therefore, the correct expansion is: $$\log_2 5 + \log_2 x$$