...both members to the rath power, we have a^ = ym; ' whence the logarithm of ym = 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...

...«'* 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 both members...

...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",...

...Nm, since mx is the exponent of that power of li.e base which is equal to Nm ; hence PROPERTY III. The logarithm of any power of a number is equal to the logu rilhm of that number multiplied by the exponent of the power. EXAMPLES. Ex. 1. Find the third...

...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...

...-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...that number multiplied by the exponent of the power. Hence, to involve a number by logarithms, we, have the following RULE. Multiply the logarithm of the...

...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 m? — (a')' or loga (m') = tx = ílogam....

...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 both members...

...have M a' _ • - - _ ^- (T* — V' N — o' " Therefore, log f ~ I = x — y = log M — log N. 11. The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take...

...second, member by member, we have ;»£«*-» N a" Therefore, log f -^ \ =x — y = log M — log 2f. 11. The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take...