1. **Stating the problem:** Convert 500 watts (W) to decibel-watts (dBW) and decibel-milliwatts (dBm) using the formula $X(\text{dB}) = 10 \log X$. 2. **Formula and explanation:** - To convert power $P$ in watts to dBW: $$P_{\text{dBW}} = 10 \log_{10}(P)$$ - To convert power $P$ in watts to dBm, first convert watts to milliwatts (1 W = 1000 mW), then use: $$P_{\text{dBm}} = 10 \log_{10}(P \times 1000)$$ 3. **Convert 500 W to dBW:** $$P_{\text{dBW}} = 10 \log_{10}(500)$$ Calculate $\log_{10}(500)$: $$\log_{10}(500) = \log_{10}(5 \times 10^2) = \log_{10}(5) + \log_{10}(10^2) = 0.69897 + 2 = 2.69897$$ So, $$P_{\text{dBW}} = 10 \times 2.69897 = 26.9897$$ 4. **Convert 500 W to dBm:** First convert 500 W to mW: $$500 \text{ W} = 500 \times 1000 = 500000 \text{ mW}$$ Then, $$P_{\text{dBm}} = 10 \log_{10}(500000)$$ Calculate $\log_{10}(500000)$: $$\log_{10}(500000) = \log_{10}(5 \times 10^5) = \log_{10}(5) + \log_{10}(10^5) = 0.69897 + 5 = 5.69897$$ So, $$P_{\text{dBm}} = 10 \times 5.69897 = 56.9897$$ **Final answers:** - $500 \text{ W} = 26.99 \text{ dBW}$ - $500 \text{ W} = 56.99 \text{ dBm}$