| Henry Burchard Fine - Algebra - 1904 - 612 pages
...and n = a", we have m/n = a* /a" = a'i-", 738 Theorem 3. The logarithm of any power of a number is **the logarithm of the number multiplied by the exponent of the power.** For if m = аf¿, we have mr = (aT)' = a*', that is, logamr = rц = r loga»i. 739 Theorem 4. The logarithm... | |
| Henry Burchard Fine - Algebra - 1904 - 616 pages
...is, lognwi/n = n — r = Iog0)u — logan. 738 Theorem 3. The logarithm, of ainj power of a number is **the logarithm of the number multiplied by the exponent of the power.** For if m = cf, we have mr = (aT-)r = a*r, that is, logamr = r/j. = r Iog0m. 739 Theorem 4. The logarithm... | |
| James Morford Taylor - Trigonometry - 1905 - 256 pages
...(AT •*• N) = x — y = log«, Af - loga.2v". (iii) The logarithm of any power of an arithmetic **number is equal to the logarithm of the number multiplied by the exponent of the power.** Let M = a*. Then, for all real values of p, we have M" = ai.*. Hence loga (Mp) = px = p loga M. (1)... | |
| John Charles Stone, James Franklin Millis - Algebra - 1905 - 792 pages
...n. Jíí Hence, log„ = x - ;/ = log„m - logaw. (E) The logarithm of a power of a number equals **the logarithm of the number, multiplied by the exponent of the power;** that is, logan»=p log,tn. To prove this, let ax=n. Then np = (a* )" = <#*». Hence, \oganp = px= p... | |
| Webster Wells - Algebra - 1906 - 484 pages
...5. log 85|. 8. log 375. 11. log Щ . 3. log11f 6. log 175. 9. logff. 12. log 2^. 423. In any system, **the logarithm of any power of a number is equal to...the number multiplied by the exponent of the power.** Assume the equation a* = m\ whence, x = 1ogam. Raising both members of the assumed equation to the... | |
| Webster Wells - Algebra - 1906 - 570 pages
...log 85f. 8. log 375. 11. log Щ . 3. log 11*. 6. log 175. 9. log ft. 12. Iog2tt423. In any system, **the logarithm of any power of a number is equal to...the number multiplied by the exponent of the power.** • Assume the equation a* = m; whence, « = logam. Raising both members of the assumed equation to... | |
| George Lisle - Accounting - 1906 - 448 pages
...positive numbers is the excess of the logarithm of the dividend over the logarithm of the divisor. (3) **The logarithm of any power of a number is equal to the logarithm of the number multiplied by the** index of the power. If m, n, and x are any numbers, these properties may be shown thus : — (1) Multiplication... | |
| George Albert Wentworth - Algebra - 1906 - 440 pages
...of a quotient is equal to the logarithm of the dividend less that of the divisor. The logarithm of a **power of a number is equal to the logarithm of the number multiplied by the exponent of the power.** EXERCISE 136 1. What is the logarithm of 24 if 24 = Юi-8802? 2. What is the logarithm of -fa ? 3.... | |
| William Findlay Shunk - Railroad engineering - 1908 - 388 pages
...logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. **The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power.** The logarithm of any root of a number is equal to the logarithm of the number divided by the index... | |
| Webster Wells - Algebra - 1908 - 470 pages
...log-2/-. 5. Iog85f. 8. log 375. 11. log 46^3. logllJ, 6. log 175. 9. log §f. 12. log 2^89. In any system, **the logarithm of any power of a number is equal to...the number multiplied by the exponent of the power.** Assume the equation a" = m ; whence, x = log, m. Raising both members of the assumed equation to the... | |
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