Math Problem Statement
With the aid of mean value theorem prove that a−b a ≤log a b ≤a−b b for0<b≤a.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Inequalities
Logarithmic Functions
Formulas
Mean Value Theorem (MVT): f'(c) = (f(a) - f(b)) / (a - b)
Logarithmic inequality: (a - b) / a ≤ log(a / b) ≤ (a - b) / b
Theorems
Mean Value Theorem
Suitable Grade Level
Advanced High School (Grades 11-12) / College Level
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