Question

The value of $\underset{x\to a}{lim}\frac{\log (x-a)}{\log (e^x-e^a)}$ is

• A. 1
• B. -1
• C. 0
• D. 2

Answer 1

Answer: (A)

1

Substitute $x=a+t$

${lim}_{t\to 0}\frac{logt}{log(e^{a+t}-e^a)}$

$=\frac{logt}{log{e}^a(e^t-c)}$

$=\frac{logt}{a+log\frac{(e^t-c)t}{t}}$

$=\frac{logt}{a+log\left(\frac{(e^{+}-1)}{t}\right)+Logt}$

$=\frac{1}{\frac{a}{logt}+1}$

$=\frac{1}{0+1}=1$