Question

expand the following.
\log_{2} 5^{2} \cdot 4^{3}
a) \log_{2} 5 - \log_{2} 4
b) 2 \log_{2} 5 + 3 \log_{2} 4
c) \log 20
d) \log 5 + 3 \log 4

Explanation:

Step1: Apply log product rule

$\log_2(5^2 \cdot 4^3) = \log_2 5^2 + \log_2 4^3$

Step2: Apply log power rule to each term

$\log_2 5^2 + \log_2 4^3 = 2\log_2 5 + 3\log_2 4$

Answer:

B) $2\log_2 5 + 3\log_2 4$