1. The problem is to evaluate $\log_{40}(3.3)$. 2. The logarithm $\log_b(a)$ answers the question: "To what power must we raise $b$ to get $a$?" 3. We use the change of base formula: $$\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$$ where $c$ is any positive number (commonly 10 or $e$). 4. Applying the formula with base 10: $$\log_{40}(3.3) = \frac{\log_{10}(3.3)}{\log_{10}(40)}$$ 5. Calculate each logarithm (using a calculator or log tables): $\log_{10}(3.3) \approx 0.5185$ $\log_{10}(40) \approx 1.6021$ 6. Divide the results: $$\frac{0.5185}{1.6021} \approx 0.3235$$ 7. Therefore, the value of $\log_{40}(3.3)$ is approximately $0.3235$.