Question

expand the following logarithmic expression into a sum or difference of logs.
\\\log_{16}(xy)\\

• \\(\log_{16}(x) \log_{16}(y)\\)
• \\(\log_{16}(x) - \log_{16}(y)\\)
• \\(\log_{16}(x) + \log_{16}(y)\\)
• \\(\frac{\log_{16}(x)}{\log_{16}(y)}\\)
• none of the above

Explanation:

Apply the product rule of logarithms

$$ \log_{b}(xy) = \log_{b}(x) + \log_{b}(y) $$

Substitute the given base

$$ \log_{16}(xy) = \log_{16}(x) + \log_{16}(y) $$

Answer:

• (A) \(\log_{16}(x) \log_{16}(y)\)
• (B) \(\log_{16}(x) - \log_{16}(y)\)
• (C) \(\log_{16}(x) + \log_{16}(y)\) (Correct answer)
• (D) \(\frac{\log_{16}(x)}{\log_{16}(y)}\)
• (E) None of the above