...mn = a**"* ; therefore, log. mn — x-\-z = log. »»-(-log. n. 4. — The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For, let «1 = 0", n = a* ; then x = log. то, z = log. m. By division we have _ _ a*-* • n therefore,...

...have mn = a*+* ; therefore, log. mn = x-\-z = log. m-|-log. и. 4. — The logarithm of q quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For, let m = a", n •=. a* ; then x = log. m, z = log. n. By division we have _ — a»-» • я...

...numbers, J which is 5 + 4. 13S. Again, a* = M and a" = N M By dividing we have a** = — . That is, The logarithm of the quotient of two numbers is equal to the difference of their logarithms, Thus, the logarithm of 100000000000 is 11. The logarithm of 100000000...

...therefore mn = a'+* ; therefore log, mn = x + y= log, m + log, n. 54. The logarithm of a, quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For let jB=log,m, and y=log.n; therefore !?? = ££=«*-»; therefore log. - =jc—y=log,m- log. n....

...equation (2), member Ъу member, we have, 10m~~" = -y or, m — n — \og-y-. hence, The logarithm of (he quotient of two numbers, is equal to the logarithm of the dividend diminished Ъу the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm of the product...

...find the number corresponding to the resulting logarithm, and it will be the product required. 397. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. If we divide Eq. (1) by Eq. (2), member by member, we shall have a x -v=~. n Therefore,...

...and n = a". Then mn = a'+s ; «'. log ти = x + y = log m + log n. 372. The logarithm of a quotient is equal to the logarithm of the dividend 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...

...therefore mn = a1 a" = et**; therefore loganm = x + y = logam + logaw. 536. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. thereforo m = a", n = a? ; ma!° therefore — = — = a"-" ; no? therefore Iog0 - =x — y = logam...

...treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Let m = a", and n=aS. Then - = o"-'; n =logant- logan. Thus the operation of Division is changed into...

...treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the dicisor. Let m=a*, and n = a". Then ™ = a"-»; •• a = log(Jm-logan. Thus the operation of Division...