...Napier, 1. The logarithm of the product of two numbers is the sum of the logarithm of each number. 2. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. 3. The logarithm of a power of a number...

...logam + log^ + \ogap + Example : log,012 = Iog,0(3 x 4) = log,03 + log,04. / \ loge [— J = logam ie the logarithm of the quotient of two numbers is equal to the difference of their logarithms. Proof : Let logam = x and logan = y :. a* = m (1) and ay = n (2). Dividing (1) by (2) we get a*~ >...

...logaq + logar + .... It should be remembered that log (m + n) # log m + log n unless m + n = mn. //. The logarithm of the quotient of two numbers is equal to the difference of their logarithms to the same base, Le., m loga ~ = loga m - loga n Proof. Dividing (1) and (2) of (I), we get, ma* "...