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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... - Page 81
by Nathan Scholfield - 1845

Edward Ira Edgerton, Perry Amherst Carpenter - Algebra - 1925 - 398 pages
...power, (a?)" = am = Mn. Hence, log0 M " = xn = n • log0 M. 6. The logarithm of a root of a number is the logarithm of the number divided by the index of the root, or, stated in symbols, Loga -\/M = - loga M. n Proof: Let x = loga M , so that a* = M. Extracting the...

## An Introduction to Statistical Analysis

George Gailey Chambers - Statistics - 1925 - 280 pages
...is also true for fractional and negative values of n. IV. The logarithm of a root of a number equals the logarithm of the number divided by the index of the root. Consider \/c and let c = kx or logic = x Then r .-. 1 xr/— 1 V c = Cr= kr or log* vc = In practice,...

## Algebra

William Raymond Longley, Harry Brooks Marsh - Algebra - 1926 - 608 pages
...0.9655 = i log 788 This example illustrates the following rule. Rule. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. General proof. IV. To prove : logb Vp = n Let P = b=, then log„P = x. Then Ур = \fa = b» . Hence,...

## The New International Encyclopędia, Volume 14

Encyclopedias and dictionaries - 1926 - 890 pages
...exponent is equal to the exponent times the logarithm of the number. 4. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. For example, to multiply 50 by 70, log (70 X 50) = log 70 -flog 6 + log lO" = 1.8451 + 0.6990+1 = 3.5441...

## College Algebra

Arthur McCracken Harding, George Walker Mullins - Algebra - 1928 - 344 pages
...the number. For Mk = (a1)* = akx. Hence logo Mk = kx = k logo M. (10) The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. For W = (a*)1/* = a*lk. Hence loga VM = xfk = r loga M . NOTE. While (6) is true, negative numbers...

## Surveying Tables

Surveying - 1940 - 412 pages
...the logarithm of the number multiplied by the exponent of the power. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. 5. Proportional parts. — Suppose it is required to find the logarithm of 2245.7. First find the mantissa...

## Mathematics for the Coast Artillery Officer

Coast Artillery School (U.S.) - 1943 - 64 pages
...the logarithm of the number multiplied by the exponent of the number. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. To find (13,000) 4: Log 13,000 = 4.11394; 4 X Log 13,000 = 16.45576; finding the antilog of 16.45576,...

## Principles and Applications of Mathematics for Communications-electronics

Electrical engineering - 1992 - 270 pages
...x_ 1 5 .7 6537 6,537 124. Finding the Root of a Number b/ Logarithms The logarithm of the root of a number is equal to the logarithm of the number divided by the root. Example 1 : Evaluate Nj/34987. log 34987 log 34900 log 34987 log 35000 87 '.00 100* x Example2:...