Use properties of logarithms to write each expression as a single logarithm. Assume that variables represent positive real numbers, with base $\neq 1$.
-$3 \log _{b} q-\log _{b} r$

A) $\log _{b} \frac{q^{3}}{r}$

B) $\log _{b} \frac{3 q}{r}$

C) $\log _{b} q^{3} \div \log _{b} r$

D) $\log _{b}\left(q^{3}-r\right)$

Question

Use properties of logarithms to write each expression as a single logarithm. Assume that variables represent positive real numbers, with base $\neq 1$.
-$3 \log _{b} q-\log _{b} r$

A) $\log _{b} \frac{q^{3}}{r}$

B) $\log _{b} \frac{3 q}{r}$

C) $\log _{b} q^{3} \div \log _{b} r$

D) $\log _{b}\left(q^{3}-r\right)$

Quizplus · Accepted Answer

Using the properties of logarithms, specifically the product rule $\log_b(m^n) = n\log_b(m)$ and the quotient rule $\log_b(m) - \log_b(n) = \log_b(\frac{m}{n})$, the expression $3 \log _{b} q-\log _{b} r$ simplifies to $\log _{b} \frac{q^{3}}{r}$.

Use Properties of Logarithms to Write Each Expression as a Single