...over the characteristic, denotes that it only is negative, as the mantissa is always positive. 368. The logarithm of a product is equal to the sum of the logarithm of its factors. For, let m and n be any two numbers, x and y their respective logarithms,...

...101. loga oo = oo. 102. (i) loga mn=\ogam + logan; (ii) logamnr ---- =logaw+loga«+logar+ ---- ; or, the logarithm of a product is equal to the sum of the logarithms of its factors. 103. or, the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm...

...and explain the reason why the tangent when determined from the cosine has two values. 3. Prove that the logarithm of a product is equal to the sum of the logarithms of its factors. 4. Shew that cot {0 + tan-1 (tans0)} = 2 cot 0. 5. Prove that sin 0 > d — — , 6 being the circular...

...Involution Multiplication, . . . Evolution Division, as we shall show in the next four Articles. 455. The logarithm of a product is equal to the sum of the logarithms of its factors. Let m = a", and n = a'. Then mn=a"+'; :. log,mn=x + y = log.m + logan. Hence it follows that logjmnp...

...Involution Multiplication, ... Evolution Division, as we shall show in the next four Articles. 455. The logarithm of a product is equal to the sum of the logarithms of its factors. No. Log 100 0000000 101 0043214 102 0086002 103 0128372 104 0170333 105 0211893 Let m=a', and n=o»....

...of Logarithms, The following properties of logarithms are demonstrated in treatises on algebra. I. The logarithm of a product is equal to the sum of the logarithms of its factors. II. The logarithm of a quotient is found by subtracting the logarithm of the divisor from that of the...

...negative infinity. 311. The use of logarithms is founded on the four following theorems. THEOREM VII. The logarithm of a product is equal to the sum of the logarithms of its factors. Proof. Let p and q be two factors, and suppose h = logjB, k = log?. Then 10* = p, 10* = q. Multiplying,...

...Iog0 1=0. 134. The logarithm of the lase itself is unity. For a1 = a, therefore logaa = 1 . 135. Tlie logarithm of a product is equal to the sum of the logarithms of its factors. For let x = log„I?i, y = logaи ; therefore m = a*, n = a0; therefore mn = a"a? = a*+y; therefore...

...distance of the second headland from the first. 6. Prove the formulae : 2 tan i September. 1. Prove that the logarithm of a product is equal to the sum of the logarithms of the factors. 2. In a system of logarithms of which the base is 9, what are the logarithms of 3, 27,...

...10 and log^ 1 0. 211. We give here a formal proof of the following propositions : To prove that (i) The logarithm of a product is equal to the sum of the logarithms of the factors. (ii) The logarithm of a quotient is equal to the difference of the logarithms of the dividend...