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 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 »

The derivative of ln(2x) is 1/x. This is due to the rules of derived logarithmic expressions, which state that the derivative of ln(ax), where "a" is any real number, is equal to 1/x. More »

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 »

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 »

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 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 »