 | George Roberts Perkins - 1850 - 356 sider
...square root of 365, we decompose 365 into the prime factors 5 and 73. Now, it is obvious that the root of the product of any number of factors is equal to the product of their roots, hence, the square root of 365 is equal to the square root of 5 x 73, which... | |
 | John Bonnycastle - 1851 - 288 sider
..."T" #"? -<fec., = log. yy'y" &c.; or, lo g- y^/', & c -; = lo g- y + lo g- y' + :1 °g- y"» &e From which it is evident, that the logarithm of the product...equal to each other, and the sum of them be denoted by m,the preceding property will then become log. y m — m log. y. From which it appears, that the logarithm... | |
 | Charles William Hackley - 1851 - 536 sider
...we shall have in a similar manner and so on. Or, in general, the logarithm of a product of several factors is equal to the sum of the logarithms of those factors separately. DIVISION. 49. Dividing the equation. V = n by the equation 6" = »' we have, observing... | |
 | Royal Military Academy, Woolwich - 1853 - 476 sider
...of 1 is 0 ; for a" =: 1. Properties of Logarithms. 1. The logarithm of the product of any number nf factors is equal to the sum of the logarithms of those factors. . Let cf = P, a" = Q, a' = R and a" = S : then we have x = log,, P, y = loga Q, z = lojra R, v = log.... | |
 | Joseph B. Mott - 1855 - 58 sider
...NxN'xN"; therefore log (NX N' X N") = x+x+x" = log N -f- bg N'+ log N". Hence we come to the conclusion that the logarithm of the product of any number of factors is equal to the sum of the logarithms of the factors (THEOREM 1.) Now if we take the logarithms of 2 and 3 as hereafter computed, we have log... | |
 | Charles Davies, William Guy Peck - 1855 - 628 sider
...for purposes of computation. Tin following properties of logarithms are common to all systems : 1 . The logarithm of the product of any number of factors, is equal to the sum of the logarithms of the factors, taken separately. 2. The logarithm of the quotient of one number by another, is ci/ual... | |
 | Elias Loomis - 1855 - 356 sider
...of the base « which is equal to NN' ; hence PROPERTY I. The logarithm of the product of two or more factors is equal to the sum of the logarithms of those factors. Hence we see that if it is required to multiply two or more numbers by each other, we have only to add their... | |
 | Elias Loomis - 1855 - 192 sider
...MULTIPLICATION BY LOGARITHMS. (11.) According to Art. 3, the logarithm of the product of two or more factors is equal to the sum of the logarithms of those factors. Hence, for multiplication by logarithms, we have the following RULE. Add the logarithms of the factors ; the... | |
 | 1863 - 746 sider
..." Surds of any degree may be simplified by application of the following principle : " " The n* root of the product of any number of factors is equal to the product of the n'1" roots of those factors." In Day's Algebra, edition- of 1848, under the head of... | |
 | Bourdon (M., Louis Pierre Marie) - 1858 - 262 sider
...is not prime, has at least one prime divisor other than unity. 3. The remainder of the division by 9 of the product of any number of factors, is equal to the remainder which the product of the remainders of the division of each factor by 9 gives. Prove that... | |
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Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence... 
