 | Earle Raymond Hedrick - Algebra - 1908 - 442 pages
...quotient is equal to the logarithm of the dividend less that of the divisor, for 10m -=- 10" = 10m~". III. The logarithm of a power of a number is equal to the...the number multiplied by the exponent, of the power, for (10™)" = 10""'. This principle includes the extraction of roots by using fractional exponents,... | |
 | William James Milne - Algebra - 1908 - 480 pages
...Involution by 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 number,... | |
 | Webster Wells - Algebra - 1908 - 456 pages
...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 logarithm of 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... | |
 | William Findlay Shunk - Railroad engineering - 1908 - 386 pages
...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 logarithm of 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... | |
 | Levi Leonard Conant - Plane trigonometry - 1909 - 290 pages
...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. mv = (10*)" = 10*y. .'. log mv = xy = y log m. 5. The logarithm of any root... | |
 | Levi Leonard Conant - Trigonometry - 1909 - 320 pages
...dividend minus the logarithm of the divisor. PROOF. n .-.tog 2n = log m — log 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? = (10*)" = 10*». .'. log m v = xy = y log m. 5. The logarithm of any... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Logarithms - 1909 - 264 pages
...x — y = loga n— loga m. (2) Manifestly loga ( . - ) = — loga m. \mj III. The logarithm of the power of a number is equal to the logarithm of the number multiplied by the index of the power. For, if x = loga n, then n = a*. Hence, np = (a1)" = ap* or, log« (n'») = px... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Plane trigonometry - 1909 - 272 pages
...log«, »— log«, m. (2) \Mfc/ Manifestly loga ( — )=» — loga m. \mJ III. The logarithm of the power of a number is equal to the logarithm of the number multiplied by the index of the power. For, if x = loga n, then n = ax. Hence, np = (a1)»1 = apx or, loga (n?) =px =... | |
 | Stimson Joseph Brown, Paul Capron - Algebra - 1910 - 212 pages
...quantities as in III, we have 2L = b * = b xv nb* or logs f-^-j = logs m - logs 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 m =• x; then m »= (6•)» = J~, or logs (mn) =nx. But... | |
 | Herbert E. Cobb - Mathematics - 1911 - 296 pages
...dividend minus the logarithm of the divisor. III. Iog2 8 = 31og2. 2 s = (10°- 8010 ) 8 = l0 °-9080 = 8. The logarithm of a power of a number is equal to the...the number multiplied by the exponent of the power. IV. log V3 = log 3* = £ log 3. -v/3 = 3* = (l0 °-4771 )* = 10°- 2888 = 1.732. The logarithm of the... | |
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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. 
