Answer:
Option 3: [tex]log_{4} (\frac{7}{m} )[/tex]
Step-by-step explanation:
Logarithmic functions represented by [tex]log_{b} x = y[/tex] means that [tex]x = b^{y}[/tex] where x > 0, b > 0, and b ≠ 1.
According to the quotient rule:
[tex]log_{b} ( \frac{M}{N} ) = log_{b}M - log_{b}N[/tex]
In the given problem, since both logs have the same base = 4, then we can model [tex]log_{4} 7 - log_{4} m[/tex] to the quotient rule, resulting in:
Quotient rule: [tex]log_{b} ( \frac{M}{N} ) = log_{b}M - log_{b}N[/tex]
[tex]log_{4}7 - log_{4}m = log_{4} ( \frac{7}{m} )[/tex]
Therefore, the correct answer is Option 3: [tex]log_{4} (\frac{7}{m} )[/tex]
