The function of ln(x*1) can be expressed using the product rule as ln(x) + ln(1). The function of ln(x^1) can use the power rule to result in 1 x ln(x). More »

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The Maclaurin series for ln(1+x) is ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + x. This series gives an approximate value of ln(1+x) when x is between minus one and one. The more terms are included, the more accurate the value... More »

In calculus, the primary significance of 1/x is its value as the derivative of the natural logarithm of "x." The proof for the derivative of ln(x) may be found by defining the inverse of the natural logarithm, expressed ... More »

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The mathematical property associated with ln x + ln y is the product rule of natural logarithms, expressed as ln(x ? y) = ln(x) + ln(y). The rule is used for adding together any two logarithm expressions that are to the ... More »

The Taylor series expansion of ln(x) around a point x = a is ln(x) = ln(a) + (x-a)/a - ((x-a)^2)/(2 a^2) + ((x-a)^3)/(3 a^3) - ... More »

The equation y = ln(x) states that y is equal to the natural logarithm of x. The natural logarithm is defined as the area under the curve of y = 1/t between t = 1 and t = x. More »

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The integral of ln(x) with respect to x is xln(x) - x + c, where c is an arbitrary constant. One can prove that this result is correct by using the method of integration by parts. More »