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).
The quotient rule is similar to the product rule and can be used to express the function ln(x/1) as ln(x) - ln(1). Since ln(x*1), ln(x/1) and ln(x^1) all equal ln(x), the function can be further evaluated. For example, given that f (x) = ln(x), the derivative of ln(x) is expressed as f'(x) = 1/x. The integral of ln(x) becomes ln(x)dx = x ∙ (ln(x) - 1) + C. The ln(x) is always undefined when x is less than or equal to zero, whereas the value of ln(x) is infinite for values of x greater than zero.