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Red_CCF
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If I take e^ln|x|, do I get x or |x|?
e^ln|x| is an expression that represents the inverse function of the natural logarithm of the absolute value of x. It is also known as the exponential function of the natural logarithm of x.
The value of e^ln|x| is always equal to the absolute value of x. This is because the natural logarithm and exponential functions are inverse operations and cancel each other out, leaving just the absolute value of x.
The vertical bar, or absolute value symbol, in e^ln|x| indicates that the input, in this case x, must be positive or negative without specifying a direction. This is because the natural logarithm of a negative number is undefined, so the absolute value ensures a valid input for the expression.
No, e^ln|x| cannot be simplified any further. This is because the inverse functions of the natural logarithm and exponential functions are the most simplified forms of these operations.
e^ln|x| is useful in many mathematical and scientific applications, such as solving exponential and logarithmic equations, modeling growth and decay, and calculating probabilities in statistics. It is also used in physics and engineering to model natural phenomena, such as radioactive decay and population growth.