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Various perspectives on a pair of simple inequalities for log x

Published online by Cambridge University Press:  11 October 2023

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
13 Sandown Road, Lancaster LA1 4LN e-mail: pgjameson@talktalk.net
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Extract

The basic inequalities

The inequalities in question are(1)

and(2)

for x > 1.

Type
Articles
Information
The Mathematical Gazette , Volume 107 , Issue 570 , November 2023 , pp. 430 - 437
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Copyright
© The Authors, 2023 Published by Cambridge University Press on behalf of The Mathematical Association

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References

Mercer, Peter R., Cauchy's mean value theorem meets the logarithmic mean, Math. Gaz. 101 (March 2017) pp. 108–115.CrossRefGoogle Scholar
Jameson, Graham and Mercer, Peter R., The logarithmic mean revisited, Amer. Math. Monthly 126 (2019) pp. 641–645.CrossRefGoogle Scholar
Jameson, G. J. O., Monotonic ratios of functions, Math. Gaz. 105 (March 2021) pp. 129–134.CrossRefGoogle Scholar