To evaluate the given expression \(\frac{\log_5 (0.04)}{\log_3 18 - \log_3 2}\), let's simplify it step by step: 1. Use the properties of logarithms to simplify the numerator: \(\log_5 (0.04) = \log_5 \left(\frac{4}{100}\right) = \log_5 \left(\frac{1}{25}\right) = \log_5 5^{-2} = -2\( 2. Use the properties of logarithms to simplify the denominator: \(\log_3 18 - \log_3 2 = \log_3 \left(\frac{18}{2}\right) = \log_3 9 = 2\( 3. Substitute the simplified values back into the expression: \(\frac{\log_5 (0.04)}{\log_3 18 - \log_3 2} = \frac{-2}{2} = -1\)