Answer:
No extraneous solution
Step-by-step explanation:
We have the logarithmic equation given by,
![\log_{2}[\log_{2}(\sqrt{4x})]=1](https://tex.z-dn.net/?f=%5Clog_%7B2%7D%5B%5Clog_%7B2%7D%28%5Csqrt%7B4x%7D%29%5D%3D1)
i.e. 
i.e. 
i.e. 
i.e. 
i.e. 
i.e. 
So, the solution of the given equation is x=4.
Now, as we domain of square root function is x > 0 and also, the domain of logarithmic function is
.
Therefore, the domain of the given function is x > 0.
We know that the extraneous solution is the solution which does not belong to the domain.
But as x=4 belongs to the domain x > 0.
Thus, x = 4 is not an extraneous solution.
Hence, this equation does not have any extraneous solution.
A). The answer is x = -4
Work:
3 - x = 11 + x
3 - x - 3 = 11 + x - 3
-x = x + 8
-x - x = x + 8 - x
-2x = 8
-2x/-2 = 8/-2
Answer: x = -4
B). The answer is x = 6
Work:
2x + 7 = 3x + 1
2x + 7 = 3x + 1 - 7
2x = 3x - 6
2x - 3x = 3x - 6 - 3x
-x = -6
-x/-1 = -6/-1
Answer x = 6
C). Answer: x = 4/3
Work:
8 - 2x = 4 + x
8 - 2x - 8 = 4 + x - 8
-2x = x - 4
-2x - x = x - 4 - x
-3x = -4
-3x/-3 = -4/-3
Answer: x = 4/3
D). Answer: x = 2
Work:
4x + 2 = 2x + 6
4x + 2 - 2 = 2x + 6 - 2
4x = 2x + 4
4x - 2x = 2x + 4 - 2x
2x = 4
2x/2 = 4/2
Answer: x = 2
Your answer should be written as two fractions, with an equal sign between them. This could help you later to solve x.
8/64 = 2/x
Again, these should be written as fractions.