Question

expand the logarithm as much as possible.\\(\log_{2}(p^{2}q)\\)\
select one:\
\\(\bigcirc\\) a. \\(\log_{2}(p^{2}) \cdot \log_{2}(q)\\)\
\\(\bigcirc\\) b. \\(2\log_{2}(p) + \log_{2}(q)\\)\
\\(\bigcirc\\) c. \\(2\log_{2}(p + q)\\)\
\\(\bigcirc\\) d. \\(\log_{2}(p^{2}) - \log_{2}(q)\\)

Explanation:

Step1: Apply product rule of logs

$\log_2(p^2q) = \log_2(p^2) + \log_2(q)$

Step2: Apply power rule of logs

$\log_2(p^2) = 2\log_2(p)$

Step3: Substitute back to expand

$2\log_2(p) + \log_2(q)$

Answer:

B. $2 \log_2(p) + \log_2(q)$