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Theorem-4 : If a, m, n are positive real numbers and a # 1, thenloga-loga m -loga n |
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Answer» Let logaM = x ⇒ ax= M and logaN = y ⇒ ay= N Now ax/ay= M/N or, ax - y= M/N Therefore from definition we have, loga(M/N) = x - y = logaM- logaN[putting the values of x and y] Corollary:loga[(M × N × P)/R × S × T)] = loga(M × N × P) - loga(R × S × T) = logaM + IogaN + logaP - (logaR + logaS + logaT) The formula of quotient rule[loga(M/N) = logaM - logaN]is stated as follows:The logarithm of the quotient of two factors to any positive base other than I is equal to the difference of the logarithms of the factors to the same base |
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