| Elias Loomis - Geometry - 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 - 126 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 - 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,... | |
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