...by p, we have, 10'' = mr ; whence, by the definition, xp = log mr (8.) That is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both members of (4), we have, 10r = whence, by the definition,...

...56.5 : x, to find x. Ans. 2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Let (1) bz =и; then, by def., log n =x. (1)*=(2) 6"x=n!'; then, by def., log n'—px. . • . log...

...division, — = a" ; n therefore, log. I — ) = x — z = log. 7W — log. n. 5. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For, let m=cf; then z = log. m. By involution, m' = a" ; therefore, log. (mr) =rx = r log. m. 6. The...

...definition, a px _ m p . px = Log m'; . . . . (7) hence, the following principle: 3°. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. If we extract any root cf both members of (3), denoted by r, we have, a r = / \/m; whence, by definition,...

...have, »•— f Hence, log ( — J = m — n, or, = log M — log N. PRIN. 6. — The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For, since if we raise both members to the nth power, we have, 10 mn _ M * f Hence, log M" = mn, or,...

...n, and dividing, member by member, we have in which x — y = loga ( —V 360. The logarithm of any power of a number is equal to the logarithm of the number, multiplied by the exponent of the power. For, assume the equation, of =zm, and raising both members to the power p, we have <ff = mp, in which...

...dividing, member by member, we have in which x — у = log„ í — V 3fiOi The logarithm of any power of a number is equal to the logarithm of the number, multiplied by the exponent of the power. For, assume the equation, ax = m, and raising both members to the power p, we have ax" = mf, in which...

...quotient is equal to the logarithm of the dividend diminished by that of the divisor. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. The logarithm of any root of a number is equal to the logarithm of the number divided by the index...

...exponent equal to 3x5; thus, (a i ) i = a 1 i, and, generally, (a") m =a nm . Hence, the logarithm of the power of a number is equal to the logarithm of the number multiplied by the exponent of the pmver. To extract the 5th root of the number a1, we write a, giving it an exponent equal to f; thus,...

...power of a given number may be found by logarithms as follows : The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. EXAMPLE.— To find the fifth power of 9, logarithm 9 = 0-954243X5 = 4-771215, and the number corresponding...