 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...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...equation (Art. 9) M=ax, then, raising both sides to the mth power, we have Mm = (a*)i" = a™ . ' Therefore, log (Mn) =xm= (log M) X m. 12. The logarithm of... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...first equation by the second, member by member, we have £=£!=«-* N ~ a" ~ Therefore, log (-^J = x — y = log M — log N. 11. The logarithm of any...let m be any number, and take the equation (Art. 9) M—cf, then, raising both sides to the mth power, we have Mm = (a*)"1 = a™ . Therefore, log (Mm)... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...9, we have Dividing the first equation by the second, member by member, we have Therefore, log (^) = x — y = log M— log N. 11. The logarithm of any...let m be any number, and take the equation (Art 9) then, raising both sides to the rath power, we have M m = (a x ) m = a™ . Therefore, log (M m ) —... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...equation by the second, member by member, we have Therefore, log TT = * ~~ y ~ log m — log ». 401 1 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 = ax ; then, raising both... | |
 | Isaac Todhunter - Algebra - 1866 - 618 pages
...loga — = x — y = logam — logan. 92> 537. T/te logarithm of any power, integral or fractional, of a, number is equal to the product of the logarithm of the number by the i/idex of the power. For let m = a*; therefore mr = (a')r — a", therefore Iog0 (mr) = xr = r Iog0... | |
 | Isaac Todhunter - Plane trigonometry - 1866 - 206 pages
...therefore log. - =jc—y=log,m- log. n. n . 55. The logarithm of any power, integral or frat tional, 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. (m') = xr = r log. m.... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...first equation by the second, member by member, we have Jf_£ --o.-». N -* o» Therefore, log I -^ I = x — y= log M — log N. 11. The logarithm of...let m be any number, and take the equation (Art. 9) If—tf, then, raising both sides to the mth power, we have Mm = (a1)" = a™ . Therefore, log (Mn)... | |
 | James Hamblin Smith - 1869 - 412 pages
...diminished by the logarithm of the divisor. Let m = a', and и = a?, Then - = a"i; n m log m - log n, 373. The logarithm of any power of a number is equal to the product of the logarithm of the number and the index denoting the power. Let m = a*. Then mr = a" = r . log m. 374. The logarithm of any root... | |
 | James Hamblin Smith - Trigonometry - 1870 - 286 pages
...1-7191323 their difference = -8508148 which is the logarithm of 7-092752, the quotient required. 146. The logarithm of any power of a number is equal to the product of the logarithm of the number and the index denoting the power. Let m = a'. Then m' = a"; .-. log m' = rx = r . log„«i. Thus the... | |
 | James Hamblin Smith - Algebra - 1870 - 452 pages
...1-7191323 their difference = -8508148 which is the logarithm of 7'092752, the quotient required. 457. The logarithm of any power of a number is equal to the product of the logarithm of the number and the index denoting the power. Let m—ax. Then mr=arx; =r.log«»i. Thus the operation of Involution... | |
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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 the equation (Art. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a""... 
