1. **State the problem:** Calculate $\frac{6.231}{(242.7)^3}$ using logarithm tables. 2. **Formula and rules:** Using logarithms, division and powers can be transformed into subtraction and multiplication: $$\log\left(\frac{a}{b^3}\right) = \log a - 3 \log b$$ 3. **Find logarithms:** - Look up $\log 6.231$ in the log table. - Look up $\log 242.7$ in the log table. 4. **Calculate:** - Multiply $\log 242.7$ by 3. - Subtract this from $\log 6.231$. 5. **Find the antilog:** - Use the antilog table to find the number corresponding to the result from step 4. 6. **Result:** - This antilog value is the answer to $\frac{6.231}{(242.7)^3}$. **Example with approximate values:** - $\log 6.231 \approx 0.7945$ - $\log 242.7 \approx 2.3856$ - Multiply: $3 \times 2.3856 = 7.1568$ - Subtract: $0.7945 - 7.1568 = -6.3623$ - Since the log is negative, add 7 to get $0.6377$ and adjust the power accordingly. - Antilog $0.6377 \approx 4.34$ - Adjusting for power of 10: $4.34 \times 10^{-7}$ So, $\frac{6.231}{(242.7)^3} \approx 4.34 \times 10^{-7}$. This method uses logarithm tables to simplify complex calculations by converting multiplication and division into addition and subtraction of logarithms.