...Multiplying these equations, member by member, We have, а.т + y==.mn, in which, x-^-y= log,, m n. 359. 77,e logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. For, assume the equations. <f = m, a3 = n, and dividing, member...

...5. The logarithm of the product of two numbers is equal to the 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 of the number...

...---- ; 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....

...geometrically the cosine of the sum of two angles whose sines and cosines are given. 3. Prove that the logarithm of a quotient is equal to the logarithm...of the dividend diminished by the logarithm of the divisor. 4. Find log '005957964, having given log 59579 = 4-7750933, log 59580 = 4"7751005. 5. Prove...

...for so long as we are treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient is equal to the, logarithm...of the dividend diminished by the logarithm of the divisor. Let m=a', and n=a'. Then "ao"~'5 = log.m — log.n. Thus the operation of Division is changed...

...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...

...0, then ^ + £ = £ + - . ß aba / JS Sol. a + fl = • ' " «48 or + = + . QED 10. — Prove that the logarithm of a quotient is equal to the logarithm...of the dividend diminished by the logarithm of the divisor. Given log. 2 = -69314718, log. 3 = 1-09861229 ; fiad the logarithms to base e of 8 /0\3e>...

...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 of a fraction is equal to...

...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" = ap« ; whence...

...^°£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 n = a", .'. y = logan. m _ a* __...