| George Roberts Perkins - 1850 - 342 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... | |
| JAMES RYAN - 1851
..."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 - 372 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
...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
...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 - 592 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 - 316 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 - 178 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
..." 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 - 248 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... | |
| |