The problem asks us to simplify the expression $log_3 a - (log_3 b + log_3 c)$ into a single logarithm.

1. Problem Description

The problem asks us to simplify the expression $log_3 a - (log_3 b + log_3 c)$ into a single logarithm.

2. Solution Steps

We can use logarithm properties to simplify the expression.

First, we simplify the expression inside the parenthesis.

The sum of two logarithms with the same base is the logarithm of the product of their arguments.

$log_x m + log_x n = log_x (mn)$

So, $log_3 b + log_3 c = log_3 (bc)$.

Now we have $log_3 a - log_3 (bc)$.

The difference of two logarithms with the same base is the logarithm of the quotient of their arguments.

$log_x m - log_x n = log_x (\frac{m}{n})$

So, $log_3 a - log_3 (bc) = log_3 (\frac{a}{bc})$.

3. Final Answer

$log_3 (\frac{a}{bc})$