Select your answer \( \begin{array}{l}\text { Which of the following is equal to } \log (x y) ? \\ \begin{array}{l}\log (x)+\log (y) \\ \log (x)-\log (y)\end{array} \\ \begin{array}{l}\frac{\log (x)}{\log (y)} \\ \log (y)-\log (y)\end{array} \\ \text { (1 out of } 6)\end{array} \)

The correct expression equivalent to \( \log(xy) \) is: \[ \log(x) + \log(y) \] **Explanation:** This follows the **product rule of logarithms**, which states that the logarithm of a product is equal to the sum of the logarithms of its factors. Mathematically, this is expressed as: \[ \log(xy) = \log(x) + \log(y) \] **Incorrect Options:** - **\(\log(x) - \log(y)\):** This represents the logarithm of a quotient, \( \log\left(\frac{x}{y}\right) \). - **\(\frac{\log(x)}{\log(y)}\):** This does not correspond to a standard logarithmic identity. - **\(\log(y) - \log(y)\):** This simplifies to 0, which is not equivalent to \( \log(xy) \). **Final Answer:** \[ \log(x) + \log(y) \]