which expression is equivalent to $log_3\frac{c}{9}$?\n$log_3 c+log_3(9)$\n$log_3(9)+log_3(c)$\n$log_3 c…

which expression is equivalent to $log_3\frac{c}{9}$?\n$log_3 c+log_3(9)$\n$log_3(9)+log_3(c)$\n$log_3 c - log_3(9)$\n$log_3(9)-log_3(c)$

which expression is equivalent to $log_3\frac{c}{9}$?\n$log_3 c+log_3(9)$\n$log_3(9)+log_3(c)$\n$log_3 c - log_3(9)$\n$log_3(9)-log_3(c)$

Answer

Explanation:

Step1: Recall logarithm quotient rule

The quotient - rule of logarithms states that $\log_a\frac{M}{N}=\log_aM-\log_aN$ for $a > 0,a\neq1,M>0,N > 0$. In the given expression $\log_3\frac{c}{9}$, we have $a = 3,M = c,N=9$.

Step2: Apply the quotient - rule

By the quotient - rule, $\log_3\frac{c}{9}=\log_3c-\log_39$.

Answer:

$\log_3c-\log_3(9)$ (the third option)