Question

Calculate ln(e^3/3).
A. 1
B. 2
C. 3
D. 1/3

Answer 1

To calculate ln(e^3/3), use the property that the natural logarithm of a number raised to an exponent is equal to the product of the exponent and the natural logarithm of the number. In this case, ln(e^3/3)=3*ln(e/3). The natural logarithm of 1/3 can be calculated as ln(1)-ln(3), so ln(e^3/3)=3*(0-ln(3))=-3*ln(3).

Step-by-step explanation:

To calculate ln(e^3/3), we can use the property that the natural logarithm of a number raised to an exponent is equal to the product of the exponent and the natural logarithm of the number. In this case, ln(e^3/3)=3*ln(e/3).

Since the natural logarithm of e is 1, we have ln(e^3/3)=3*ln(e/3)=3*ln(1/3).

The natural logarithm of 1/3 can be calculated as ln(1)-ln(3). Since ln(1)=0, we have ln(e^3/3)=3*ln(1/3)=3*(0-ln(3))=-3*ln(3).