Evaluate the following limits :
`lim_(x to 1)(x-1)/(logx)`.

Answer

To evaluate the limit \( \lim_{x \to 1} \frac{x - 1}{\log x} \), we can follow these steps:

### Step 1: Identify the form of the limit
First, we need to substitute \( x = 1 \) into the expression:
\[ \frac{1 - 1}{\log 1} = \frac{0}{0} \]
This is an indeterminate form (0/0), which means we can apply L'Hôpital's Rule.

### Step 2: Apply L'Hôpital's Rule
According to L'Hôpital's Rule, if we have an indeterminate form of type \( \frac{0}{0} \), we can differentiate the numerator and the denominator separately.

- The derivative of the numerator \( x - 1 \) is:
\[ \frac{d}{dx}(x - 1) = 1 \]

- The derivative of the denominator \( \log x \) is:
\[ \frac{d}{dx}(\log x) = \frac{1}{x} \]

### Step 3: Rewrite the limit
Now we can rewrite the limit using the derivatives:
\[ \lim_{x \to 1} \frac{x - 1}{\log x} = \lim_{x \to 1} \frac{1}{\frac{1}{x}} = \lim_{x \to 1} x \]

### Step 4: Evaluate the limit
Now we can substitute \( x = 1 \) into the simplified expression:
\[ \lim_{x \to 1} x = 1 \]

### Final Answer
Thus, the value of the limit is:
\[ \boxed{1} \]