If a^{3-x}b^{5x}=a^{x+5}b^{3x}, prove that \displaystyle x\ln{\frac{b}{a}}=\ln{a}.

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Examples 2a, Question 9, p. 22)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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