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Decreasing property of ratio of two logarithmic expressions involving tangent function.

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Title: Decreasing property of ratio of two logarithmic expressions involving tangent function.
Authors: Qi, Feng1,2 (AUTHOR), Agarwal, Ravi Prakash3 (AUTHOR), Lim, Dongkyu4 (AUTHOR) dklim@anu.ac.kr
Source: Mathematical & Computer Modelling of Dynamical Systems. Dec2025, Vol. 31 Issue 1, p1-16. 16p.
Subjects: Logarithms, Tangent function, Differentiable functions, Ratio & proportion, Mathematics, Logic, Monotonic functions
Abstract: In this article, the authors review three proofs of the decreasing property of the ratio of two logarithmic expressions. With the help of the monotonicity rule for the ratio of two differentiable functions, the authors provide an alternative proof of the decreasing property of the ratio of two logarithmic expressions. These logarithmic expressions involve the tangent function. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:In this article, the authors review three proofs of the decreasing property of the ratio of two logarithmic expressions. With the help of the monotonicity rule for the ratio of two differentiable functions, the authors provide an alternative proof of the decreasing property of the ratio of two logarithmic expressions. These logarithmic expressions involve the tangent function. [ABSTRACT FROM AUTHOR]
ISSN:13873954
DOI:10.1080/13873954.2024.2449322