natural logarithmic function
[natural logarithmic function|natural logarithmic function] is the inverse of the natural exponential function, expressed as y = logex or Inx.
Definition
natural logarithmic function is the inverse of the natural <a href='/en/entity/exponential-function'>exponential function</a>, expressed as y = logex or Inx.
Mechanism
natural logarithmic function The natural logarithmic function y = Inx = logex is defined alongside the natural <a href='/en/entity/exponential-function'>exponential function</a> y = e^x. Theorem 3.15 states that its derivative for x > 0 is given by equation (3.30). More generally, differentiable functions g(x) can be applied to the logarithmic function.
Effects
natural logarithmic function Differentiating the natural logarithmic function allows finding derivatives of y = log,x and y=b* for b>0,b# 1. The inverse hyperbolic functions involve the natural logarithm as a result.