Given:
Heat loss from the fin = 6W
Effectiveness of the fin = 3
Efficiency of the fin = 0.75

To find:
Heat loss from the fin when the entire fin surface is at base temperature.

Solution:

Step 1: Understanding the terms
Before we proceed with the solution, let's understand what effectiveness and efficiency mean in the context of heat transfer.

- Effectiveness: It is the ratio of actual heat transfer from the fin to the maximum possible heat transfer from the fin. Mathematically, effectiveness (ε) is given by:
ε = Actual heat transfer from the fin / Maximum possible heat transfer from the fin

- Efficiency: It is the ratio of actual heat transfer from the fin to the heat input to the fin. Mathematically, efficiency (η) is given by:
η = Actual heat transfer from the fin / Heat input to the fin

Step 2: Finding the maximum possible heat transfer
To find the heat loss from the fin when the entire fin surface is at base temperature, we need to find the maximum possible heat transfer from the fin. This can be calculated using the formula:
Maximum possible heat transfer = Heat input to the fin x Efficiency

Since the efficiency of the fin is given as 0.75, we can express the maximum possible heat transfer as:
Maximum possible heat transfer = Heat input to the fin x 0.75

Step 3: Calculating the heat input to the fin
To calculate the heat input to the fin, we can use the formula:
Heat input to the fin = Heat loss from the fin / Efficiency

Since the heat loss from the fin is given as 6W and the efficiency is given as 0.75, we can substitute these values to find the heat input to the fin:
Heat input to the fin = 6W / 0.75 = 8W

Step 4: Finding the heat loss from the fin
Now that we have the heat input to the fin, we can substitute this value in the formula for the maximum possible heat transfer to find the heat loss from the fin when the entire fin surface is at base temperature:
Heat loss from the fin = Heat input to the fin x Efficiency
Heat loss from the fin = 8W x 0.75 = 6W

Therefore, the heat loss from the fin, keeping the entire fin surface at base temperature, is 6W.

Conclusion:
The heat loss from the fin, when the entire fin surface is at base temperature, is 6W. Therefore, the given answer range of '7.9, 8.1' is incorrect.