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" The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. "
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... - Page 256
by Charles Davies - 1854 - 432 pages
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...mn = a**"* ; therefore, log. mn — x-\-z = log. -(-log. n. 4. — The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For, let 1 = 0", n = a* ; then x = log. то, z = log. m. By division we have _ _ a*-* • n therefore,...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...have mn = a*+* ; therefore, log. mn = x-\-z = log. m-|-log. и. 4. — The logarithm of q quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For, let m = a", n •=. a* ; then x = log. m, z = log. n. By division we have _ — a- • я...
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Algebra: Adapted to the Course of Instruction Usually Pursued in the ...

Paul Allen Towne - Algebra - 1865 - 314 pages
...numbers, J which is 5 + 4. 13S. Again, a* = M and a" = N M By dividing we have a** = — . That is, The logarithm of the quotient of two numbers is equal to the difference of their logarithms, Thus, the logarithm of 100000000000 is 11. The logarithm of 100000000...
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Trigonometry for Beginners: With Numerous Examples

Isaac Todhunter - Plane trigonometry - 1866 - 206 pages
...therefore mn = a'+* ; therefore log, mn = x + y= log, m + log, n. 54. The logarithm of a, quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For let jB=log,m, and y=log.n; therefore !?? = =*-; therefore log. - =jc—y=log,m- log. n....
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Elements of Surveying and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1866 - 422 pages
...equation (2), member Ъу member, we have, 10m~~" = -y or, m — n — \og-y-. hence, The logarithm of (he quotient of two numbers, is equal to the logarithm of the dividend diminished Ъу the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm of the product...
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A Treatise on Algebra

Elias Loomis - Algebra - 1868 - 386 pages
...find the number corresponding to the resulting logarithm, and it will be the product required. 397. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. If we divide Eq. (1) by Eq. (2), member by member, we shall have a x -v=~. n Therefore,...
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A Treatise on Elementary Algebra

James Hamblin Smith - 1869
...and n = a". Then mn = a'+s ; '. log ти = x + y = log m + log n. 372. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Let m = a', and и = a?, Then - = a"i; n m log m - log n, 373. The logarithm of any power of a number...
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Algebra for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - Algebra - 1870 - 608 pages
...therefore mn = a1 a" = et**; therefore loganm = x + y = logam + logaw. 536. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. thereforo m = a", n = a? ; ma! therefore — = — = a"-" ; no? therefore Iog0 - =x — y = logam...
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Elementary algebra

James Hamblin Smith - 1870
...treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Let m = a", and n=aS. Then - = o"-'; n =logant- logan. Thus the operation of Division is changed into...
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Elementary Algebra

James Hamblin Smith - Algebra - 1870
...treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the dicisor. Let m=a*, and n = a". Then ™ = a"-; •• a = log(Jm-logan. Thus the operation of Division...
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