Question

which of the following is equivalent to \\(\log 9w\\)? \\(\log 9 - \log w\\) \\(\log 9 + \log w\\) \\(9(\log w)\\) \\(w(\log 9)\\)

Explanation:

Step1: Recall the product rule of logarithms

The product rule of logarithms states that for any positive numbers \( a \), \( b \), and base \( c \) (where \( c>0 \), \( c
eq1 \)), \( \log_c(ab)=\log_c a+\log_c b \).

Step2: Apply the product rule to \( \log(9w) \)

Here, \( a = 9 \) and \( b = w \), and assuming the same base for the logarithm (the base is not specified, but the rule holds for any valid base). So, by the product rule, \( \log(9w)=\log 9+\log w \).

Answer:

\( \log 9 + \log w \) (the second option)