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a<(b-a)/ln(b/a)<b
$latex \displaystyle \left(\frac{1}{b}\right)(b-a) < \int_a^b \frac{1}{x} dx < \left(\frac{1}{a}\right)(b-a)$, for positive $latex a, b>a$ $latex \displaystyle\implies \frac{b-a}{b} < \…