A) 1
B) ?1
C) 0
D) None of these
Correct Answer: A
Solution :
\[\underset{\text{x}\to a}{\mathop{\text{lim}}}\,\,\,\frac{\log \,(x-a)}{\log \,({{e}^{x}}-{{e}^{a}})}=\underset{\text{x}\to a}{\mathop{\text{lim}}}\,\,\,\frac{{{e}^{x}}-{{e}^{a}}}{(x-a)\,{{e}^{x}}}\], \[\left( \text{Form}\frac{0}{0} \right)\] \[=\underset{x\to a}{\mathop{\lim }}\,\,\,\frac{{{e}^{x}}}{\left\{ (x-a)\,{{e}^{x}}+{{e}^{x}} \right\}}=\frac{{{e}^{a}}}{{{e}^{a}}}=1.\]
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