Given,

, we need to find value of n

So we will first find the limit and then equate it with 108 to get the value of n.

We need to find the limit for:

As limit can’t be find out simply by putting x = a because it is taking indeterminate form(0/0) form, so we need to have a different approach.

Let, Z =

Note: To solve the problems of limit similar to one in our question we use the formula mentioned below which can be derived using binomial theorem.

Formula to be used:

As Z matches exactly with the form as described above so we don’t need to do any manipulations–

Z =

Use the formula:

∴ Z = n(3)^n–1

According to question Z = 108

∴ n(3)^n–1 = 108

To solve such equations, factorize the number into prime factors and try to make combinations such that one satisfies with the equation.

⇒ n(3)^n–1 = 4× 27 = 4× (3)^4–1

Clearly on comparison we have –

n = 4