Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers.
-$\log _{13}\left(\frac{14 m}{n}\right)$

A) $\frac{\log _{ 13}14+\log _{ 13} m}{\log _{ 13} n}$

B) $\log _{ 13}14+\log _{ 13}m-\log _{ 13} n$

C) $(\log_{ 13}14)(\log _{ 13} m)-\log _{ 13} n$

D) $\log 1314-\log _{ 13} m-\log _{ 13} n$

Question

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers.
-$\log _{13}\left(\frac{14 m}{n}\right)$

A) $\frac{\log _{ 13}14+\log _{ 13} m}{\log _{ 13} n}$

B) $\log _{ 13}14+\log _{ 13}m-\log _{ 13} n$

C) $(\log_{ 13}14)(\log _{ 13} m)-\log _{ 13} n$

D) $\log 1314-\log _{ 13} m-\log _{ 13} n$

Quizplus · Accepted Answer

The quotient rule for logarithms states that $\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)$, and the product rule states that $\log_b(xy) = \log_b(x) + \log_b(y)$. Applying these rules to $\log _{13}\left(\frac{14 m}{n}\right)$ results in $\log _{13}14 + \log _{13}m - \log _{13}n$.

Rewrite in Terms of Two or More Logarithms Using the Quotient