| Charles Davies - Algebra - 1860 - 412 pages
...members of equation (1) to the nth power, we have, But from the definition, we have, nx' = log (N'") ; **that is, The logarithm of any power of a number is equal to** t)ie logarithm of the number multiplied by the exponent of the power. 233. If we extract the »'* root... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...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... | |
| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...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... | |
| Charles Davies - Algebra - 1863 - 338 pages
...members of ( 3 ) to any power denoted by p, we have, Whence, by definition, px = Log mf . . . (1.) **That is, the logarithm of any power of a number is...the number multiplied by the exponent of the power.** If we extract any root of both members of ( 3 ), denoted by r, we have, ar = Whence, by definition,... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...Raising both members of (4) to the power denoted by JP, we have, whence, by the definition, xp = log mp **(8.) That is, the logarithm of any power of a number is equal to the logarithm of** tJie number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...member by member, we have £=£!=«-* N ~ a" ~ Therefore, log (-^J = 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... | |
| Benjamin Greenleaf - Algebra - 1864 - 420 pages
...equation by the second, member by member, we have Therefore, log TT = * ~~ y ~ log m — log ». 401 1 **The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power.** For, let m = ax ; then, raising both members to the rth power, we have mr = (<f)r = a*". Therefore,... | |
| Benjamin Peirce - Algebra - 1864 - 298 pages
...&c. = log. m -\- log. m -\- log. m -f- &c, or Logarithm or Root, Quotient, and Reciprocal. that 1s, **the logarithm of any power of a number is equal to...the number multiplied by the exponent of the power.** 12. Corollary. If we substitute in the above equation, it becomes M log. p = n log. v/ p, log. ^p=!°gP;... | |
| Elias Loomis - Algebra - 1864 - 386 pages
...logarithm ol Nm, since mx is the exponent of that power of the base which s equalt) Nm; hence PROPERTY III. **The logarithm of any power of a number is equal to the** toga rithm of that number multiplied by the exponent of the power. EXAMPLES. Ex. 1. Find the third... | |
| Edward Brooks - Geometry - 1868 - 284 pages
...second, we have, .Zv Hence, log ( — J = m — n, or, = log M — log N. 1o»-»=.3[ PRIN. 6. — **The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power.** For, since 10* =M, if we raise both members to the rath power, we have, 10"- = JM* Hence, log M n =... | |
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