ln |u| + c
The expression ln |u| + c represents the natural logarithm of the absolute value of the variable u, plus a constant c
The expression ln |u| + c represents the natural logarithm of the absolute value of the variable u, plus a constant c.
The natural logarithm, denoted as ln, is the logarithm with base e, where e is a mathematical constant approximately equal to 2.71828. It is the inverse function of the exponential function y = e^x.
When you take the natural logarithm of a positive number, the result is a positive value. However, when you take the natural logarithm of a negative number, the result is not a real number. That’s why the absolute value of the variable u (|u|) is used in the expression ln |u| + c.
Adding a constant c at the end allows for more general solutions. The constant c can be any real number, and it shifts the graph of the function upwards or downwards along the y-axis.
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