Subjects algebra

Dbw Hz Calculation 8A701F

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

Use the AI math solver

1. **State the problem:** Calculate the value of $-204$ dBW/Hz $+ 8$ dB $+ 10 \log 2000000$. 2. **Recall the formula:** The expression involves logarithms and addition of decibel values. The key formula is $10 \log_{10}(x)$ for converting power ratios to decibels. 3. **Calculate $10 \log 2000000$:** $$10 \log 2000000 = 10 \log (2 \times 10^6) = 10 (\log 2 + \log 10^6) = 10 (0.3010 + 6) = 10 \times 6.3010 = 63.01$$ 4. **Add all terms:** $$-204 + 8 + 63.01 = (-204 + 8) + 63.01 = -196 + 63.01 = -132.99$$ 5. **Final answer:** $$\boxed{-132.99 \text{ dBW/Hz}}$$ This means the combined value is approximately $-133$ dBW/Hz.