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Βιβλία Βιβλία 21 - 30 από 103 για The logarithm of any power of a number is equal to the logarithm of the number multiplied....
" The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. "
A Theoretical and Practical Arithmetic: In which the Principles of that ... - Σελίδα 233
των Bézout - 1825 - 236 σελίδες
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Treatise on Algebra, for the Use of Schools and Colleges

William Smyth - 1855 - 336 σελίδες
...both members to the rath power, we have a^ = ym; ' whence the logarithm of ym = mx = m log y. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the exponent of the power. To form any power whatever of...

Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies, M. Bourdon (Louis Pierre Marie) - 1857 - 400 σελίδες
...«'* power, we have, a*.' = N'n (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...

A Treatise on Algebra

Elias Loomis - 1858 - 359 σελίδες
...Nm, since mx is the exponent of that power of li.e base which is equal to Nm ; hence PROPERTY III. The logarithm of any power of a number is equal to the logu rilhm of that number multiplied by the exponent of the power. EXAMPLES. Ex. 1. Find the third...

A Treatise on Algebra: For the Use of Schools and Colleges

William Smyth - 1858
...both members to the with power, we have a~ = 1r; whence the logarithm of y m = mx = m log y. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the exponent of the power. To form any power whatever of...

A treatise on plane and spherical trigonometry, and on trigonometrical ...

John Hymers - 1858
...diminished by that of the divisor. Since m — a", n = a", m a_ i fm\ ii .'' S" (n) = X~y= g" m ~ g° n' 9. The logarithm of any power of a number is equal to the product of the logarithm of the number by the index of the power. Since m = a", .: mr = (a*)" = a",...

An elementary treatise on logarithms

William Henry Johnstone - 1859 - 55 σελίδες
...n, or x = loga m, y = loga я l ,vm ax then — = — = a'.v, n ae = \ogam-logan. 7. ln any system, the logarithm of any power of a number is equal to...logarithm of that number multiplied by the index of that power. Let a' — m, or x = loga m ¡ then m? — (a')' or loga (m') = tx = ílogam. 8. ln any...

ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY

ELIAS LOOMIS, LL.D. - 1859
...-0.4753 divided by -36.74. INVOLUTION BY LOGARITHMS. (14.) It is proved in Algebra, Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. Hence, to involve a number by logarithms, we, have the following RULE. Multiply...

Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - 1860 - 400 σελίδες
...power, we have, a«' = N'a ..... (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...

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 σελίδες
...have M a' _ • - - _ ^- (T* — V' N — o' " Therefore, log f ~ I = x — y = log M — log N. 11. The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take...

Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 σελίδες
...second, member by member, we have ;»£«*-» N a" Therefore, log f -^ \ =x — y = log M — log 2f. 11. The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take...




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