On the approximation of logarithms of algebraic numbers
Kurt Mahler · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences · 1953
Abstract A new identity is given by means of which infinitely many algebraic functions approximating the logarithmic function In x are obtained. On substituting numerical algebraic values for the variable, a lower bound for the distance of its logarithm from variable algebraic numbers is found. As a further application, it is proved that the fractional part of the number ea is greater than a-40a for every sufficiently large positive integer a.