Power Series

If y=10^{x}, show by taking logarithms to base e that y=e^{x\ln{10}}.  Hence, write down the first 4 terms in the expansion of 10^{x}.

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Examples 3a, Question 12, p. 39)

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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