Subjects algebra

Logarithm Calculation 51E1D1

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Calculate the value of $$D$$ given the formula $$D = 2.75 \times \log A - \sqrt{\frac{1}{A}}$$ where $$A = 7.7$$ million. 2. **Write the formula and explain:** The formula is $$D = 2.75 \times \log A - \sqrt{\frac{1}{A}}$$. - $$\log A$$ means the logarithm of $$A$$ (base 10). - $$\sqrt{\frac{1}{A}}$$ means the square root of the reciprocal of $$A$$. 3. **Substitute the value of $$A$$:** $$D = 2.75 \times \log 7.7 - \sqrt{\frac{1}{7.7}}$$ 4. **Calculate $$\log 7.7$$:** $$\log 7.7 \approx 0.8865$$ 5. **Calculate the square root term:** $$\sqrt{\frac{1}{7.7}} = \sqrt{0.12987} \approx 0.36$$ 6. **Calculate the product:** $$2.75 \times 0.8865 = 2.438$$ 7. **Put it all together:** $$D = 2.438 - 0.36 = 2.078$$ 8. **Final answer:** $$\boxed{D = 2.078}$$ million. This means the value of $$D$$ is approximately 2.078 million.