*Question E4D13:
What is the received signal level with a transmit power of 10 W (+40 dBm), a transmit antenna gain of 6 dBi, a receive antenna gain of 3 dBi, and a path loss of 100 dB?*  

*Correct Answer is  A: -51 dBm*  

### AI Response: (may contain errors)  

To determine the received signal level, we use the following formula:

$$
\text{Received Signal Level (dBm)} = P_T + G_T + G_R - L
$$

where:
- $P_T$ = transmit power in dBm
- $G_T$ = transmit antenna gain in dBi
- $G_R$ = receive antenna gain in dBi
- $L$ = path loss in dB

Given:
- Transmit power $P_T = +40 \, \text{dBm}$
- Transmit antenna gain $G_T = 6 \, \text{dBi}$
- Receive antenna gain $G_R = 3 \, \text{dBi}$
- Path loss $L = 100 \, \text{dB}$

Substitute these values into the formula:

$$
\text{Received Signal Level} = 40 + 6 + 3 - 100 = -51 \, \text{dBm}
$$

### Explanation of the Correct Answer:
- **Correct Answer: -51 dBm (Choice A)**  
  The calculation shows that the received signal level is indeed -51 dBm, which matches choice A.

### Explanation of Incorrect Choices:
- **Choice B: -54 dBm**  
  This result would occur if there was an error in the calculation, such as using incorrect values for gains or path loss.

- **Choice C: -57 dBm**  
  This would be the result if the gains were underestimated or the path loss was overestimated.

- **Choice D: -60 dBm**  
  This would be the result if there was a significant error in the calculation, such as ignoring one of the antenna gains.

### Key Points:
- Always convert all power and gain values to dBm and dBi before using them in the formula.
- Ensure that path loss is subtracted, as it represents a reduction in signal strength.