...logarithm of the product of any number of factors is equal to the sum of the logarithms of the factors. (2) The logarithm of the quotient of two numbers is equal to the logarithm of the numerator diminished by the logarithm of the denominator. (4) The logarithm of the rth root of a number...

...numbers to a common base represent exponents of the same number, it follows that: 576. PRINCIPLE. — The logarithm of the quotient of two numbers is equal...of the dividend minus the logarithm of the divisor ; that is, To any base, log (m ч- и) = log m — log п. For, let loga m = x and log,, n = у, ч...

...numbers to a common base represent exponents of the same number, it follows that: 576. PKIXCIPLK. — The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minn» the logarithm of the divisor ; that is, To any base, log (?» -=-«) = log m — log n. For,...

...y = log n. (Art. 438) Substituting in (3), log mn = log m + log n. 454. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. Let 10* = m (1) and 10» = n. (2) Dividing (1) by (2), jg = m. That is, 1O"-» = — • n Whence,...

...a" Therefore, loga ( — ) =x — y = loga m — logя и, \я/ that is, the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. Thus Raising both sides of the equation a* = m to the ktii power, where k is any real number, integral...

...calculation : ( 1 ) The logarithm of a product is equal to the sum of the logarithms of its factors. (2) The logarithm of the quotient of two numbers is equal to the logarithm of the dividend less the logarithm of the divisor. (3) The logarithm of a number affected by an exponent is equal to...

...This law may evidently be extended to any finite number of factors. II. The logarithm of the quotient is equal to the logarithm of the dividend minus the logarithm of the divisor, all to the same base. For, if x = logaw and y = loga »и, we may write as before, n = a?, m = av....

...respectively. Then mn= 10* -10"= 10X+V. •'• log(wm) = x + y = log m + log n. 3. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. .'. log ~ — x — y — log m — log n. n 4. The logarithm of any power of a number is equal to...

...This law may evidently be extended to any finite number of factors. II. The logarithm of the quotient is equal to the logarithm of the dividend minus the logarithm of the divisor, all to the same base. For, if x = loge n and y = loga то, we may write as before, n = a1, m = ay....

...logarithms respectively. Then .'. log(ran) = x + y = log m + log n. 3. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. PROOF. n .-.tog 2n = log m — log n. 4. The logarithm of any power of a number is equal to the logarithm...