| Charles William Hackley - Algebra - 1849 - 504 pages
....-. by definition, nx is the logarithm of N" ; that is to say, The logarithm of any power of a given **number is equal to the logarithm of the number multiplied by the exponent of the power.** IV. Extract the n" 1 root of both members of equation (1). ii N°=u". x i .-. by definition, - is the... | |
| Benjamin Peirce - Algebra - 1851 - 284 pages
...-\- log. m -{- log. m -(- &c. or Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm **of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power.** or 12. Corollary. If we substitute m in the above equation, it becomes n log. p = n log. v' p, log.... | |
| A. M. LEGENDRE - 1852
...n , in which m X n is the logarithm of M n (Art. 1) : hence, The logarithm of any power of a given **number is equal to the logarithm of the number multiplied by the exponent of the power.** 16. Taking the same equation, i(F=M, and extracting the nib. root of both members, we have n m 1 10... | |
| ELIAS LOOMIS, A.M. - 1852
...is the exponent of that power of the base which is equal to N wl ; hence PROPERTY III. The logarithm **of any power of a number is equal to the logarithm of** that number multiplied by the exponent of the power. EXAMPLES. Ex. 1. Find the third power of 4 by... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1854 - 432 pages
...=M a , in which mX n is the logarithm of M" (Art. 1) : hence, The logarithm of any power of a given **number is equal to the logarithm of the number multiplied by 'the exponent of the power.** 16. Taking the same equation, W'" = M, and extracting the nth root of both members, we have m 1 10"=JIf»'... | |
| Benjamin Peirce - Algebra - 1855 - 288 pages
...-f- log. m -j- log. m -J- &c. or Logarithm of Root, Quotient, anil Reciprocal. that is, the logarithm **of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power.** or 12. Corollary. If we substitute m in the above equation, it becomes log. p — n log. log. VP =... | |
| JOSEPH B. MOTT. - 1855
...log a ; and if n = -, then log a m = - log a : mm r —r 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 3 4 = 4 log 3 = 4X. 477121 — 1.908484.... | |
| Elias Loomis - Algebra - 1855 - 316 pages
...mx is the exponent of that power of the base which is equal to N"; hence PROPERTY III. The logarithm **of any power of a number is equal to the logarithm of** that number multiplied by the exponent of tfie power. EXAMPLES. Ex. 1. Find the third power of 4 by... | |
| Benedict Sestini - Algebra - 1857 - 216 pages
...xc; but from a*= z, we have x = lz; hence, lz° = 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 of the equations a* = z, we will have 5 I and... | |
| Benjamin Peirce - Algebra - 1858 - 284 pages
...-(- log. m -\- log. m -{- &c. or Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm **of any power of a number is equal to the logarithm...the number multiplied by the exponent of the power.** 12. Corollary. If we substitute p = m n , or in the above equation, it becomes n log. p = n log. v'... | |
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