1. **State the problem:** Calculate the value of the expression $$D = 2.75 \times \log 7.7 - \left(\frac{1}{7.7}\right)^{0.5}$$ where $\log$ denotes the logarithm base 10. 2. **Recall the formulas and rules:** - The logarithm base 10 of a number $x$ is written as $\log x$. - The square root of a number $a$ is $a^{0.5}$. - Multiplication and subtraction follow standard arithmetic rules. 3. **Calculate each part step-by-step:** - Calculate $\log 7.7$: $$\log 7.7 \approx 0.8865$$ - Multiply by 2.75: $$2.75 \times 0.8865 = 2.438\text{ (approx)}$$ - Calculate the square root term: $$\left(\frac{1}{7.7}\right)^{0.5} = \sqrt{\frac{1}{7.7}} = \frac{1}{\sqrt{7.7}}$$ - Calculate $\sqrt{7.7}$: $$\sqrt{7.7} \approx 2.7749$$ - So the square root term is: $$\frac{1}{2.7749} \approx 0.3604$$ 4. **Combine the results:** $$D = 2.438 - 0.3604 = 2.0776$$ 5. **Final answer:** $$\boxed{D \approx 2.08}$$