Find the value of x , where x is an integer

# Find the value of x , where x is an integer

1. A
2
2. B
4
3. C
9
4. D
13

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### Solution:

We have to find the value of x in  . Let us simplify this equation.
We know that  . Hence, we can write the above equation as

Now, we can write 8 in terms of power as  . Hence,

We know that . Hence, the above equation can be written as

Now, let us take  outside the numerator. We will get

We can write this as

Let us cancel the common factors from numerator and denominator. We will get

Let us take the denominator to the RHS. We will get

We can now solve the RHS by cancelling the common factors.

Now, let us write 8 in terms of powers of 2. We will get

We know that . Hence, we can write the above expression as

We have studied that . So the above expression becomes

We know that if the bases are equal on both the sides, then their powers are equal. Hence,

By solving this, we will get
x = 4
Hence the value of x is 4.
So, the correct Ans is “Option 2”.

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