The equation y = \ln(x) represents the natural logarithm of x . The natural logarithm is the inverse function of the exponential function e^x , where e is approximately 2.718. This means that if y = \ln(x) , then x = e^y . The function is defined for x > 0 and approaches negative infinity as x approaches zero. The graph of y = \ln(x) is a curve that passes through the point (1, 0) and increases slowly as x increases. It is always increasing but never touches the x-axis, indicating that the logarithm of 1 is zero. The function is commonly used in mathematics, science, and engineering, particularly in calculations involving growth rates and decay processes.