 | Elias Loomis - Conic sections - 1877 - 458 pages
...numbers. Also, since powers of the same quantity are divided by subtracting their exponents, the logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. Since the logarithm of 10 is 1, if a number be multiplied... | |
 | Webster Wells - Logarithms - 1878 - 124 pages
...log 2 + 2 X log 3 = 0.903090 + 0.954242 — 1.857332. 13. In any system, the logarithm of n fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Assume the equations, a* = m ) ( x = log„ m \ whence, \ , a'J — n\ ' I y = loga и »~. ... a*... | |
 | Webster Wells - Algebra - 1879 - 468 pages
...15552. 3. log 56. 6. log 567. 9. log 504. 12. log 14406. 456. In any system the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Assume the equations, a* = m) , fж = loga m > whence. < -' 6" a' — nj ' \y = \ogan ... a* mm D1v1d1ng.... | |
 | Webster Wells - Algebra - 1880 - 498 pages
...15552. 3. logSG. 6. log 567. 9. log 504. 12. log 14406. 456. In any system the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denom inator. Assume the equations, al = m\ whence, /* = |°вa» = nj \y = bga ... а* т т Dividing,... | |
 | Henry Nathan Wheeler - Logarithms - 1882 - 60 pages
...x 102-0899 ; .-. logw 12300 = 2 + 2.0899 = 4.0899. § 7. In any system the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Proof: If I = bx, m = b>, then is logti = ж, logbm = у ; now — = - = b*-* ; .-. log»— = x —... | |
 | Webster Wells - Trigonometry - 1883 - 234 pages
...Iogl5552. 3. Iog56. 6. Iog567. 9. Iog504. 12. log 14406. 96. In any system the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Assume the equations whence, a" = n ) ty = logaw ТА- -л- a" m , „ m Dividing, — = — , or a*~*... | |
 | Robert Hamilton Pinkerton - Trigonometry - 1884 - 194 pages
...logarithm of the divisor; or (what is the same thing differently expressed) the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. III. The logarithm of the power, positive or negative, of a number — the root of a number being considered... | |
 | Henry Law - 1884 - 568 pages
...the logarithms of m and n is the logarithm of their product. PROPOSITION N. THEOREM. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend, with the logarithm of the divisor subtracted from it. Let X and I denote the same as in the... | |
 | Webster Wells - Algebra - 1885 - 382 pages
...4771, log 5 =.6990, log 7 = .8451 ; find the values of the following : 344. The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Assume the equations 10*= wence y=logn. =w}; whence, = ?! ) Dividing, = or 10— = -• 10" nn VYL... | |
 | Webster Wells - Algebra - 1885 - 370 pages
...4771, log 5 =.6990, log 7 = .8451 ; find the values of the following : 344. The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Assume the equations 10*=ml; whence, {^«gm. 10* = n ) ty = logn. Dividing, g_-.,1(,-'_5. _,, . m Whence,... | |
| |
N .-. by definition, x — x" is the logarithm of ^ ; that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation... 
