 The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log  Plane Trigonometry - Page 177by Levi Leonard Conant - 1909 - 183 pagesFull view - About this book
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...Multiplying equations, member by member, we have Therefore, log (MX N) — x+y = log Jf+log N. 10. The logarithm of a QUOTIENT is equal to the logarithm of the dividend diminished by that of the divisor. For, by Art. 9, we have M= a", AT = a>. Dividing the first equation... | |
 | Horatio Nelson Robinson - Algebra - 1863 - 432 pages
...But by multiplication we have 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.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...Multiplying equations, member by member, we have Therefore, log (M X N) = x -f- y = log Jf-f log ^ 10. 7%e logarithm of a QUOTIENT is equal to the logarithm of the dividend diminished by that of the divisor. For, by Art. 9, we have Dividing the first equation by the second,... | |
 | Isaac Todhunter - Plane trigonometry - 1866 - 216 pages
...log. m, and y — log. n ; therefore m = a*, and n — a'; therefore nin = therefore log. mn = 54. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For let x=\og,m, and y=\og,n; therefore m=a", andn=o»;... | |
 | James Hamblin Smith - 1869 - 412 pages
...of its factors. Let m = a', 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... | |
 | Isaac Todhunter - Algebra - 1870 - 626 pages
...therefore m = a*, n = a"; 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 — = — =... | |
 | James Hamblin Smith - Algebra - 1870 - 478 pages
...for so long as we are 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.... | |
 | Charles Davies - Leveling - 1871 - 448 pages
...Dividing (4) by (5), member by member, we have, whence, by the definition, 10*- = -; n P ~ 9 = That is, the logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. 7. Raising both members of (4), to a power denoted by t, we have,... | |
 | Adrien Marie Legendre - Geometry - 1871 - 490 pages
...( 5 ), member by member, we have, whence, by the definition, «-y = "*(£) ..... ('.) That is, <Ae logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. 7. Raising both members of (4) to the power denoted by p, we have,... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...member by member, we have, .»- = : • whence, by the definition, x - y = log (^j ..... (1.) That is, the logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. 1. Raising both members of (4) to the power denoted by p, we have,... | |
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