Lim X → a Log X − Log a X − a - Mathematics

Question

$lim_{x \to a} \frac{\log x - \log a}{x - a}$

Solution

$lim_{x \to a} [\frac{\log x - \log a}{x - a}]$
$= lim_{x \to a} [\frac{\log (\frac{x}{a})}{a (\frac{x}{a} - 1)}]$
$= lim_{x \to a} [\frac{\log [1 + (\frac{x}{a} - 1)]}{a (\frac{x}{a} - 1)}]$
$x \to a$
$∴ \frac{x}{a} \to 1$
$\Rightarrow \frac{x}{a} - 1 \to 0$
$L e t y = \frac{x}{a} - 1$
$x \to a$
$∴ y \to 0$
$= lim_{y \to 0} [\frac{\log (1 + y)}{a \times y}]$
$= \frac{1}{a} \times 1$
$= \frac{1}{a}$

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Concept of Limits - Limits of Polynomials and Rational Functions

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Q 19 Q 18 Q 20

Chapter 29: Limits - Exercise 29.1 [Page 71]

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RD Sharma Mathematics [English] Class 11

Chapter 29 Limits
Exercise 29.1 | Q 19 | Page 71

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Lim X → a Log X − Log a X − a - Mathematics

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