Question

Evaluate: $\underset{x\to 0}{lim}\log \left|\frac{\log (1+x)}{x}\right|$

• A. $0$
• B. $1$
• C. $e$
• D. $\frac{1}{e}$

Answer 1

The correct option is A $0$

Given: $\underset{x\to 0}{lim}\log \left|\frac{\log (1+x)}{x}\right|$

$\Rightarrow \log \underset{x\to 0}{lim}\left|\frac{\log (1+x)}{x}\right|$

$\Rightarrow \log 1......(\because \underset{x\to 0}{lim}\left|\frac{\log (1+x)}{x}\right|=1)$

$\Rightarrow 0$