| Earle Raymond Hedrick - Algebra - 1908 - 421 pages
...logarithm of the dividend less that of the divisor, for 10 m -s-10" = 10"'"". III. The logarithm of a **power of a number is equal to the logarithm of the number multiplied by the exponent of the power,** for (10" 1 )" = 10'"". This principle includes the extraction of roots by using fractional exponents,... | |
| Frederick Howland Somerville - Algebra - 1908 - 407 pages
...log m and y = log log — = log m — log n. n 1 (3) n. (Art. 438) (Art. 438) 455. The logarithm of a **power of a number is equal to the logarithm of the number multiplied by the exponent of the power.** Let 10* = m. (1) Raising both members of the equation to the ptb. power, 10i™ = mP. Whence, log m*>... | |
| William James Milne - Algebra - 1908 - 464 pages
...logarithms. Since logarithms are simply exponents, it follows that: 584. Principle. — The logarithm of a **power of a number is equal to the logarithm of the number multiplied by the** index of the power; that is, To any base, log m" = n log m. For, let log„ m = x, and let n be any... | |
| William James Milne - Algebra - 1908 - 464 pages
...logarithms. Since logarithms are simply exponents, it follows that : 584. PRINCIPLE. — The logarithm of a **power of a number is equal to the logarithm of the number multiplied by the** index of the power ; that is, To any base, log m" = n log m. For, let log, m = x, and let n be any... | |
| John Charles Stone - 1908
...Hence, log a — = x — y = logo TO — log a n. III. 77; e logarithm, of a power of a number equals **the logarithm of the number, multiplied by the exponent of the power** For, let a* — n. Then, nt = (a*)f = af. Hence, log a w =px =p log a w. IV. The logarithm of a root... | |
| John Charles Stone - 1908
...n Hence, logo ™ = x — y = logo m — log a n. III. The logarithm of a power of a number equals **the logarithm of the number, multiplied by the exponent of the power** For, let a 1 = n. Then, nr = (a*)' = af. Hence, Iog 0 nr=px=p logo n. IV. The logarithm of a root of... | |
| Levi Leonard Conant - Plane trigonometry - 1909 - 183 pages
...dividend minus the logarithm of the divisor. .'. log ~ — x — y — log m — log n. n 4. The logarithm **of any power of a number is equal to the logarithm of the number multiplied by the** index of the power. PROOF. m v = (10*)" = 10* y . .'. log m v = xy = y log m. 5. The logarithm of any... | |
| Stimson Joseph Brown, Paul Capron - Algebra - 1910 - 191 pages
...divisor. or Using the same quantities as in III, we have logs f —J = logs m — logo n. V. The logarithm **of any power of a number is equal to the logarithm of the number multiplied by the** index of the power. Let ,_ . m=b x , or logs rn = x; then m «= (5«). = 6 « or i og6 ( TO ») =nx... | |
| Herbert E. Cobb - Mathematics - 1911 - 274 pages
...logarithm of the divisor. III. log 2 s = 3 log 2. 98 _ /]n0.8010\8 _ ^QO.9080 _ Q The logarithm of a **power of a number is equal to the logarithm of the number multiplied by the exponent of the power.** IV. log V3 = log 3* = i- log 3. V3 = 3* = (10 0 - 4771 )* = 10 0 - 2886 = 1.732. The logarithm of the... | |
| Webster Wells, Walter Wilson Hart - Algebra - 1912 - 424 pages
...or a rt = M f . .: logM" = px. Therefore, . log M"=plog, M. Rule. — In any system, the logarithm **of any power of a number is equal to the logarithm of the number multiplied by the exponent** indicating the power. EXAMPLE 1. Given log 7 = .8451, find log 7 5 . SOLUTION : log 7 5 = 5 log 7 =... | |
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