Evaluate `lim_(xto1) "sec" (pi)/(2^(x)).log_(e)x`.

Explanation

To evaluate the limit \( \lim_{x \to 1} \sec\left(\frac{\pi}{2^x}\right) \log_e x \), we can follow these steps:

### Step 1: Substitute \( x = 1 \)
First, we substitute \( x = 1 \) into the expression:
\[ \sec\left(\frac{\pi}{2^1}\right) \log_e(1) = \sec\left(\frac{\pi}{2}\right) \cdot 0 \]
Since \( \log_e(1) = 0 \) and \( \sec\left(\frac{\pi}{2}\right) \) is undefined (infinity), we have an indeterminate form of \( \infty \cdot 0 \).
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