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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...
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 81
by Nathan Scholfield - 1845 - 232 pages

## Bonnycastle's Introduction to Algebra: Containing the Indeterminate and ...

John Bonnycastle - Algebra - 1851 - 288 pages
...Hence, the logarithm of a fraction, or of the quotient arising from dividing one number by another, is equal to the logarithm of the numerator minus the logarithm of the denominator. And if each member of the common equation a? — y be raised to the fractional power denoted by —...

## Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 410 pages
...logarithm of the quotient. The same principle may be expressed otherwise thus, the logarithm of a fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator. From this article, and the preceding, we see that by means of logarithms, the operation of Multiplication...

## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...equation (2), member by member, we have, mn MM 10 -=_r~0r, ra — tt = log-r^: hence, The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm...

## Elements of Surveying and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1852 - 412 pages
...by equation (2), member by member, we have, MM 10m n = i^or, m — n = logjr: hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm...

## Rudimentary Treatise on Logarithms

Henry Law - Logarithms - 1853 - 84 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 / denote the same as in the...

## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...equation (1) by equation (2), member by member, we have, JO™ »BB_OTjW_Wesi0g— : hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm...

## Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1854 - 446 pages
...equation (1) by equation (2), member by member, we have, 10m~n = -^or, m — n~logj^: hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm...

## Mathematical Key: New Combinations in Respect to the Binomial Theorem and ...

Joseph B. Mott - Algebra - 1855 - 58 pages
...log 6 = log^ — loga; therefore, log 2 = log p — log a : a that is, the logarithm of a fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator. (THEOREM 2.) Or, for a more general theorem for fractions, let us resume the equation log ^ — log...