Question

Which of the following is equivalent to log9(xy)?

1) log9(x) + log9(y)
2) log9(x) - log9(y)
3) log9(x) * log9(y)
4) log9(x / y)

Answer 1

The equivalent expression for log9(xy) is option 1) log9(x) + log9(y), based on the logarithmic property that the log of a product equals the sum of the logs of the individual numbers.

Step-by-step explanation:

The question is asking to find the equivalent expression of log9(xy). According to logarithmic rules, the logarithm of a product of two numbers is the sum of the logarithms of each number separately. Hence, this property can be stated as log(xy) = log(x) + log(y), regardless of the base of the logarithm. Therefore, the equivalent expression for log9(xy) is log9(x) + log9(y). Thus, the correct choice from the given options is 1) log9(x) + log9(y).