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Find the value of x , where x is an integer

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answer is B.

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Detailed Solution

We have to find the value of x in Question Image

. Let us simplify this equation.
We know that

. Hence, we can write the above equation as
Question Image

Now, we can write 8 in terms of power as

. Hence,

We know that

. Hence, the above equation can be written as
Question Image

Now, let us take

outside the numerator. We will get
Question Image

We can write this as
Question Image

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

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

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

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

We know that

. Hence, we can write the above expression as

We have studied that

. So the above expression becomes
Question Image

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

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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