Canadian Journal of Pure & Applied Sciences

Abstract: Logarithms were defined for real positive numbers with a real positive base, but were later extended to real negative numbers with a real positive base. Logarithms of real negative numbers to a real positive base were defined as complex numbers. The Neparian logarithms take into consideration the hyperbola transcribed by the function f(x) = 1/x, x>0 for real positive axis. On a parallel analogy, we extend this concept to the real negative axis for the hyperbola transcribed by 1/x for x<0. This paper examines the concept of logarithms from its basics to prove that the logarithms of real negative numbers to real negative base are real numbers. The concept of logarithms as applicable to both real positive and real negative numbers has been generalized.