The Natural Logarithm Function – Properties And Applications In Mathematics And Science



The expression ln(x) is the natural logarithm function of x. It is a mathematical function that gives the logarithm – or exponent to which the number e (approximately equal to 2.71828) must be raised to obtain the value of x.

Here are some key points to keep in mind about the natural logarithm function:

– The domain of ln(x) is all positive real numbers (x > 0), as the value of the logarithm is undefined for any negative number or zero.
– The range of ln(x) is all real numbers (-∞ < y < ∞). - The graph of ln(x) is a curve that starts at (1,0) and increases infinitely as x grows larger. - Some common properties of ln(x) include ln(1) = 0, ln(e) = 1, and ln(xy) = ln(x) + ln(y). - ln(x) is often used in mathematical analysis, calculus, and various branches of science to model functions that have exponential or logarithmic growth rates. Overall, the natural logarithm is an important function in mathematics and is used in many fields of study.

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