# Lim X → 2 X − 2 Log a ( X − 1 ) - Mathematics

$\lim_{x \to 2} \frac{x - 2}{\log_a \left( x - 1 \right)}$

#### Solution

$\lim_{x \to 2} \left[ \frac{x - 2}{\log_a \left( x - 1 \right)} \right]$

Let x = 2 + h

x → 2
∴ h → 0

$= \lim_{h \to 0} \left[ \frac{\left( 2 + h \right) - 2}{\frac{\log \left\{ \left( 2 + h \right) - 1 \right\}}{\log a}} \right]$
$= \log a \lim_{h \to 0} \left[ \frac{h}{\log \left( 1 + h \right)} \right]$
$= \log a \times 1$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Exercise 29.1 | Q 10 | Page 71