...logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. II. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor; or (what is the same thing differently expressed) the logarithm...

...factors. 625. Similarly by division whence by definition lm lo&» n = xy, - loga»t-loga«, (2) or the logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. 626. Again, with the same notation, if m = a*, it follows that m"...

...log (MxN). Or, log ( M x Л) - log M+ log N. PRIN. 4. The logarithm of the quotient of two numbers ù equal to the logarithm of the dividend minus the logarithm of the divisor. For, let m = log M, and n = log N. Then, B" = M, B*=N. Dividing, S^~jn = MiN. Hence, log ( M •*•...

...Then, (509), a^N' (1), a»"=N" (2). Multiply (1) by (2), member by member. II. The logarithm of any quotient is equal to the logarithm of the dividend, minus the logarithm of the divisor. Divide (1) (I) by (2), member by member. III. The logarithm of any power of a quantity is equal to...

...Prove that, if a ft are the roots of the equation ax* + (a + b}x + b = o, . /3 a . b 10. Prove that the logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Given loge 2 = '69314718, log,. 3 = 1-09861229 ; find the...

...The logarithm of the product of twp numbers is equal to tb* sum of the logarithms of the numbers. « The logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. The logarithm of any power of a number is equal to the logarithm...

...^°£a dwnp ... ) = tc + y + z + ... - loga m + loga n + \ogap + ... . 256. Logarithm of a Quotient. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Let m be the dividend, and let n be the divisor, and let...

...use are as follows: The logarithm of a product is equal to the sum of the logarithms of its factors: The logarithm of a quotient is equal to the logarithm...the dividend. minus the logarithm of the divisor. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the index...

...use are as follows: The logarithm of a product is equal to the sum of the logarithms of its factors. The logarithm of a quotient is equal to the logarithm of the dividend, minus tJte logarithm of the divisor. The logarithm of any power of a number is equal to the logarithm of...

...log. n + log. p. In the same way the theorem can be extended to any number of factors. 106. Theorem 2. The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. щ Let — be the quotient, a the base ; we have...