Logarithmic Functions

Prove that:

    \[\log_{a}{x}=\log_{b}{x}\times\log_{a}{b}\]

Find the value of \log_{e}{\left(0.0367^{3.757}\right)} correct to 3 significant figures, taking e=2.718.

Source: Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Miscellaneous Examples, Question 2, p. 33)

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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