...Multiplying equations, member by member, we have Therefore, log (M X N) = x -f- y = log Jf-f log ^ 10. 7%e logarithm of a QUOTIENT is equal to the logarithm of the dividend diminished by that of the divisor. For, by Art. 9, we have Dividing the first equation by the second, member by member,...

...multiplication we 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»-»...

...log. m, and y — log. n ; therefore m = a*, and n — a'; therefore nin = therefore log. mn = 54. The logarithm of a quotient is equal to the logarithm...of the dividend diminished by the logarithm of the divisor. For let x=\og,m, and y=\og,n; therefore m=a", andn=o»; therefore ™ = *=a"-'; n a° therefore...

...of its factors. Let m = a', 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...

...for so long as we are 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...

...therefore m = a*, n = a"; 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 —...

...Dividing (4) by (5), member by member, we have, whence, by the definition, 10*- = -; n P ~ 9 = That is, the logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. 7. Raising both members of (4), to a power denoted by t, we have, l0* = m'; whence,...

...( 5 ), member by member, we have, whence, by the definition, «-y = "*(£) ..... ('.) That is, <Ae logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. 7. Raising both members of (4) to the power denoted by p, we have, 10'f = mp ;...

...г = log. n. But by multiplication we have mn = a**" ; therefore, log. mn = x-\-z = log. m-)-log. n. 4. — The logarithm of a quotient is equal to the...logarithm of the dividend diminished by the logarithm bf the divisor. For, let m = a*, n = a* ; then x = log. w», z = log. n. By division we have _ = a*-*...

...member by member, we have, .»- = : • whence, by the definition, x - y = log (^j ..... (1.) That is, the logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor. 1. Raising both members of (4) to the power denoted by p, we have, = m r whence,...