 | Charles William Hackley - Algebra - 1846 - 542 pages
...N""=a°. x ! .-. by definition, - is the logarithm of N" ; that is to say, The logarithm of any root of a given number is equal to the logarithm of the number divided by the index of the root. Combining the last two cases, we shall find whence — is the logarithm... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...members, we have m _! 10n=ifn' i in which - ig ^e logarithm of M n : that is, n The logarithm of the root .of a given number is equal to the logarithm of the number divided by the index of the root. EXAMPLES. 1. What is the 5th power of 9? Log 9. =0.954243; 0.954243x5-4.771215;... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...root of both members, we have HI which - is tne logarithm of M" : that is, n The logarithm of the root of a given number is equal to the logarithm of the number divided by the index of the root. EXAMPLES. 1. What is the oth power of 9 ? Log 9 = 0.954243 ; 0.954243... | |
 | Benjamin Peirce - Algebra - 1855 - 308 pages
...r= n log. m ; Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 12. Corollary. If we substitute p — ran, in the above equation, it becomes log. p = n log. v/ p,... | |
 | Joseph B. Mott - Algebra - 1855 - 58 pages
...T —Y and if n = -, then losam = - losa : m ° m that is, the logarithm of any power or root of a number is equal to the logarithm of the number multiplied by the exponent ....... , ------ ----------- --------- (THEOREMS.) 1. log 81 = log 34 = 4 log 3 = 4X. 477121 = 1.908484.... | |
 | Charles Davies - Algebra - 1857 - 408 pages
...(5). But from the definition, we have, nx' — log (N/n) ; that is, The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 233. If we extract the nth root of both members of equation (1), we shall have, , a" -(N')~n- *JW -... | |
 | Benedict Sestini - Algebra - 1857 - 258 pages
...xc ; but from a"= z, we have x = lz ; hence, l.<f= cl.z; that is, The logarithm of the power of any number is equal to the logarithm of the number multiplied by the exponent. But if we take the root of the degree c of both members and consequently, lz' = - = -x; - x 1 cc now... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...we have m _. 10" =M~a' ± in which - is the logarithm of M" : that is, n The logarithm of the root of a given number is equal to the logarithm of the number divided by the index of the root. EXAMPLES. 1. What is the 5th power of 9? Log 9 = 0.954243 ; 0.954243... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...(5). But from the definition, we have, nx' — log (N'*) ; that is, The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 233. If we extract the nth root of both members of equation {1), we shall have, a" =(N')*= \fW - -... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...exponent equal to 3x5; thus, (a")i=ali, and, generally, (a")m=anm. Hence, the logarithm of the power of a number is equal to the logarithm of the number multiplied by the exponent of the power. To extract the 5th root of the number a', we write a, giving it an exponent equal to f ; thus, v/as=a?,... | |
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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
