Answer:
Option c is correct
[tex]\log_2 (\frac{3}{2})[/tex]
Step-by-step explanation:
Using the logarithmic rules:
[tex]\log_b (mn) = \log_b m+ \log_b n[/tex]
[tex]\log_b \frac{m}{n} = \frac{\log_b m}{\log_b n}[/tex]
Given the expression:
[tex]\log_2 6 + \log_2 2 - \log_2 8[/tex]
Apply the logarithmic rules:
[tex]\log_2 (6 \cdot 2)-\log_2 8[/tex]
Simplify:
[tex]\log_2 12 -\log_2 8[/tex]
Apply the logarithmic rules we have;
[tex]\log_2 \frac{12}{8} = \log_2 (\frac{3}{2})[/tex]
Therefore, the single logarithmic expression that is equivalent to the one shown [tex]\log_2 6 + \log_2 2 - \log_2 8[/tex] is, [tex]\log_2 (\frac{3}{2})[/tex]
