As we need to find

We can directly find the limiting value of a function by putting the value of the variable at which the limiting value is asked if it does not take any indeterminate form (0/0 or ∞/∞ or ∞-∞, .. etc.)

Let Z

∴ We need to take steps to remove this form so that we can get a finite value.

TIP: Most of the problems of logarithmic and exponential limits are solved using the formula and

This question is a direct application of limits formula of exponential and logarithmic limits.

To get similar forms as in a formula, we move as follows-

As x→2 ∴ x-2 →0

Let x-2 = y

∴ Z =

We can’t use the formula directly as the base of log is we need to change this to e.

Applying the formula for change of base-

We have-

∴ Z =

Use the formula:

∴ Z =

Hence,