...have log. 20 =x+l, log. 20000 = log. 2000=a;+3, log. 2000000=, &c. We have seen, in Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied bv the exponent of the power. Hence, log. 4 =2x, log. 32 = log....

...to t-tie with power, n mx 7V T m . U • JV f whence the logarithm of N" = mz ==m log. N. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the expo* nent of the power. •ogarithms, we multiply the logarithm of the proposed...

...«'* power, we have, a*.' = N'n (5). But from the definition, we have, nx' — log (N/n) ; 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. 233. If we extract the nth root of...

...diminished by that of the divisor. Since m — a", n = a", m a_ i fm\ ii .'' S" (n) = X~y= g" m ~ g° n' 9. The logarithm of any power of a number is equal to the product of the logarithm of the number by the index of the power. Since m = a", .: mr = (a*)" = a", .'. log„ (m') =rx = r log„ »»?, where r...

...both members to the with power, we have a~ = 1r; whence the logarithm of y m = mx = m log y. That is, the logarithm of any power of a number is equal to the product of the logarithm of this number by the exponent of the power. To form any power whatever of a number by means of a table...

...n, or x = loga m, y = loga я l ,vm ax then — = — = a'.v, n ae = \ogam-logan. 7. ln any system, the logarithm of any power of a number is equal to the logarithm of that number multiplied by the index of that power. Let a' — m, or x = loga m ¡ then...

...-0.4753 divided by -36.74. INVOLUTION BY LOGARITHMS. (14.) It is proved in Algebra, Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. Hence, to involve a number by logarithms,...

...therefore log. — = x — y = log. m — log. n. 138. The logarithm of any power, integral or fractional, of a number is equal to the product of the logarithm of the number by the index of the power. For let m = a* ; therefore m' = (»')' = a", therefore log. (mr) = xr = r log....

...power, we have, a«' = N'a ..... (5). But from the definition, we have, nx' — log (N'*) ; 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. 233. If we extract the nth root of...

...difference between the logarithm of the dividend and the logarithm of the divisor ; and the logarithm of the power of a number is equal to the product of the logarithm of the number by the exponent of the power ; and the logarithm of any root of a number is equal to the logarithm of the number divided by the...