...neither a nor b nor c will hold its usual place among the letters. — 13 QUESTIONS FOR 1866. J. Prove that the logarithm of a product is equal to the sum of the logarithms of the factors. In the common system of logarithms, what is the effect (1) of adding 1 to the logarithm, (2) of moving...

...logarithm of m to the base a. In the four following Articles, we shall suppose the base to be a. 371. The logarithm of a product is equal to the sum of the logarithms of its factors. Let m = a', and n = a". Then mn = a'+s ; «'. log ти = x + y = log m + log n. 372. The...

...log A + log В log -£- = log A — log В log Am = m log A log -pX = -i- log A, or at full length: the logarithm of a product is equal to the sum of...factors; the logarithm of a quotient is equal to the difference of the logarithms of the Dividend and of the Divisor, the logarithm of a power is equal...

...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 — = — =...

...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....

...real logarithm. For, since the base a is positive, all its powers must be positive (Art. 202). 399. The logarithm of a product is equal to the sum of the logarithms of its factors. For, let\ m = a", and n = a" ; then, multiplVing these equations, member by member, we...

...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,...

...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,...

...may be exactly divisible by the divisor, and make a proper compensation. The logarithm of a product = the sum of the logarithms of the factors. The logarithm of a quotient = the logarithm of the dividend minus the logarithm of the divisor. To find the logarithm of a number...

...the following quantities (to six significant figures): (0x26534)^ V/(0.0357635) III. 1. Prove that the logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 2. Find, by logarithms, the values of the following quan*-•...