The natural logarithm of x, denoted as ln(x), equals zero when x is equal to 1. This is because the natural logarithm is the inverse function of the exponential function with base e.
To understand why ln(1) = 0, consider the definition of a logarithm: ln(x) answers the question, ‘To what power must e be raised to obtain x?’. When we set x to 1, we are looking for the power to which e must be raised to yield 1.
Since any number raised to the power of 0 equals 1, we conclude that e^0 = 1. Therefore, we can assert that ln(1) = 0.
In summary, the natural logarithm of x equals zero when x = 1.