For 10 points, name this function that is the inverse of the exponential with base e.
The alternating harmonic series converges to this function of two; that fact can be proven using the Mercator series, a special Taylor series for this function. The integral of the tangent of x is equal to this function of the secant of x. That identity is a special case of the identity that the integral of f prime of x over f of x, dx, is equal to (*) this function of f of x. The derivative of this function is one over x. For 10 points, name this function that is the inverse of the exponential with base e.
The alternating harmonic series converges to this function of two; that fact can be proven using the Mercator series, a special Taylor series for this function.
{natural logarithm} [prompt on {logarithm}]