Question

which of the following is equivalent to log9w?
○ log9 + logw
○ log9 - logw
○ w(log9)
○ 9(logw)

Explanation:

Step1: Recall Logarithm Product Rule

The product rule of logarithms states that for any positive numbers \(a\), \(b\), and base \(c\) (where \(c>0\), \(c
eq1\)), \(\log_{c}(ab)=\log_{c}(a)+\log_{c}(b)\). Here, we assume the base is the same (usually base 10 or \(e\) if not specified), and our expression is \(\log(9w)\), which can be thought of as \(\log(9\times w)\).

Step2: Apply the Product Rule

Using the product rule \(\log(ab)=\log(a)+\log(b)\) with \(a = 9\) and \(b=w\), we get \(\log(9w)=\log(9)+\log(w)\).

Answer:

\(\log9+\log w\) (corresponding to the first option)