...of a right-angled triangle, in which the perpendicular is 127 and the hypotenuse 325. 9. Prove that the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers themselves. Find A, when 10 tan^ = 7 sin 15° 30'. 10. In the triangle ABC, if B = 57° 45', C = 105°...

...m, ai = n. Multiplying these equations, member by member, We have, in which, x 4- y = Ioga m n. 359. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For, assume the equations, a* = wi, ai — n, and dividing, member...

...Multiplying these equations, member by member, We have, in which in which, x -\- y = loga m n. 359. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For, assume the equations, ax = m, a" = n, and dividing, member...

...---- ; 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 of the divisor. 104. loga m"=n loga m; n being integral or fractional. _ i j. 105....

...following general proofs to the base a should be noticed. I. The logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm,...

...explanations are only wearying and unsatisfactory at best. The principle is, simply stated, the theorem that the logarithm of the product of two numbers is equal to the sum of their logs. The size of the dial will of course regulate the length of the calculation. The instrument...

...Dividing, N-^-N' = b 1 -x' whence it appears (Art. 384) that x —x' is. the logarithm of N+N'. Hence The logarithm of a quotient is equal to the logarithm of the dividend less the logarithm of the divisor. 393- To find the logarithm of a power. Let N=lS. Taking the m lb...

...3 when the base is 10? Ans. 0.001. § 6. In any system the logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. Proof: If l = b", m = by, n = b', then is log6Z = x, Iog6m = 2/, logbn = z; now IX mxn = b* x Ъ»...

...calculated to 7 decimal places. 66. Properties of Logarithms. I. The 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...

...member, we have, a*+y — mrii Whence, from the definition, x + y = Log mn . . . . ( 5.) i That is, the logarithm of the product of two numbers is equal to the sum of the logarithms of the tiw numbers. If we divide ( 3 ) by ( 4 ), member by member, wo shall have, m a*-* — -• n Whence,...