Step 1 :The problem is asking for the natural logarithm of the fourth root of e to the power of 3.
Step 2 :The natural logarithm of a number is the exponent to which the base e must be raised to produce that number.
Step 3 :The fourth root of a number is the number that would have to be multiplied by itself 4 times to get the original number.
Step 4 :The exponent of e in the expression is 3.
Step 5 :We can simplify the expression inside the logarithm first. The fourth root of e to the power of 3 is the same as e to the power of 3/4.
Step 6 :Then, we can take the natural logarithm of e to the power of 3/4.
Step 7 :The natural logarithm of e to the power of x is just x.
Step 8 :So, the natural logarithm of e to the power of 3/4 is 3/4.
Step 9 :Final Answer: \(\boxed{0.75}\)