equals (a ≠ b)

Concept:

L’Hospital’s Rule:

It is a general method to evaluate indeterminate forms like 0/0 or 8/8.

It can be applied multiple times until the problem is not indeterminate anymore.

Mathematically, we can write the following,

If = or  or any other indeterminate forms,

For these cases, the following is true,

= .

This is called L'Hospital's Rule.

f'(x) and g'(x) are the first order of f(x) and g(x) respectively.

If  also comes indeterminate, then the rule is further applied to obtain the second-order derivatives for f(x) and g(x).

The rule is applied until some finite value of the limit is obtained.

Calculation:

Given:

The function is .

  = .

Applying L’Hospital’s Rule, the function will become .

Now  = = log_ba

Hence, the correct answer is option 3.