 The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.  Higher Algebra - Page 415by George Egbert Fisher, Isaac Joachim Schwatt - 1901 - 615 pagesFull view - About this book
 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...an; therefore, log. (mr) = rx = r log. m. 6. — The logarithm of any root of a number ù equal to the logarithm of the number divided by the index of the root. For, let то = a1 ; then x = log. от. • By evolution we have \Ara = <f ', x log. m therefore, loar.... | |
 | Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...10r, (N)r = (10*)' = 10" .-. rx is the Log. of (N)r ie, Log. (N) =. rx = r Log. N. 4. The Log. of the root of a number is the Logarithm of the number divided by the quantity expressing the root. For, since N = 10*, (N)? = (10 }-' = 10? /. - is the Log of (N)' /. Log.... | |
 | Paul Allen Towne - Algebra - 1865 - 314 pages
...126, ex. 20, the m* root of the equation, a" = M * m is a" = VM. That is, The logarithm of the tn"' root of a number is the logarithm of the number divided by m. Thus, the logarithm of 10000000000 is 10, and the logarithm of the 1 . 1nn • *> ftth root of 10000000000,... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...Hence, log M n = mn, or, = log M X n. PRIN. 7. — The logarithm of the root of any number is equal to the logarithm of the number divided by the index of the root. For, since 10" = M, if we take the nth root of both members, we have, Hence, log .\/~M= — , or, log 3f-f-... | |
 | Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...log tj/"y7and x = log y. Hence «lo That is, the logarithm of the m"1 root of a number is equal to the logarithm of the number divided by the index of the root. LOQABITHlfS. 5 and then finding in the tables the number whoso logarithm is equal to the sum or difference,... | |
 | Edward Olney - Trigonometry - 1885 - 222 pages
...m?- Whence a» is the logarithm of the zth power of m- Q- в- D12 Prop 4:, — The logarithm of any root of a number is the logarithm of the number divided by the number expressing the degree of the notDEM Let a be the base, and x the logarithm of m- Then ax —... | |
 | Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...10", (N)" = (10*}' = 1o™ .'. rx is the Log. of (N)r ie, Log. (N/ = rx = r Log. N. 4. The Log. of the root of a number is the Logarithm of the number divided by the quantity expressing the root. For, since N = 10*, (N); = (10*)' = Ю' x * .-. - is the Log of (N)'... | |
 | Charles Davies - Leveling - 1871 - 448 pages
...the definition, I = log j/^. ...... (9.) That is, the logarithm of any root of a number, is equal to the logarithm of the number divided by the index of the root. The preceding principles enable ns to abbreviate the operations of multiplication and division of numbers,... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...= m". Whence a;z is the logarithm of the zth power of m. QED 12. Prop. 4. — The logarithm of any root of a number is the logarithm of the number divided by the number expressing the degree of the root. DEM. Let a be the base, and x the logarithm of m. Then ax... | |
 | Edward Olney - Trigonometry - 1872 - 216 pages
...= 7»'. Whence xz is the logarithm of the zth power of m. QED 12. Prop. 4. — The logarithm of any root of a number is the logarithm of the number divided by the number expressing the degree of the root. DEM Let a be the base, and x the logarithm of m. Then a*... | |
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