INTRODUCTION ΤΟ USE OF LOGARITHMS, BY EUGENE L. RICHARDS, B. A., TO ACCOMPANY GILLESPIE'S TABLES OF LOGARITHMS OF NUMBERS. A INTRODUCTION. ART. 1. DEFS.-The logarithm of any proposed number is the exponent of the power to which some fixed number must be raised in order to equal the proposed number. A system of logarithms is, therefore, a system of powers of some fixed number. The fixed number is the base of the system. The system of logarithms which is used in this book is Briggs's "System," or the common system of logarithms, and has 10 for its base. Thus : 102 = 100, 2 is the logarithm of 100 to the base 10. Or, 2 = log. 100, "to the base 10" being understood. 2. The logarithm of 1 is 0. For 1 = = 101-110°. 10 3. The logarithm of 10, or the logarithm of the base is 1. For 101 = 10. Applying fractional exponents to the first member of this equation, and extracting the square root of the second member, we have (1) 10% = 100.5 = 3.16228 (nearly). Extracting the square root of (1), (2) 10% = 100.25 = 1.77828 (nearly). |