Answer
-2
Work Step by Step
$\log_3 100$ - $\log_3 18$ - $\log_3 50$
To keep it even we apply the Second Law of Logarithms to $\log_3 100$ - $\log_3 50$
$\log_3 \frac{100}{50}$ - $\log_3 18$
$\log_3 2$ - $\log_3 18$
Apply the Second Law of Logarithms again
$\log_3 \frac{2}{18}$
$\log_3 \frac{1}{9}$
$\log_3 \frac{1}{3^2}$
Move the denominator to the numerator with a negative exponent
$\log_3 3^{-2}$
= -2