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Slav-nsk [51]
3 years ago
7

How many extraneous solutions exist for the logarithmic equation below if it is solved in the most efficient way possible?log_(2

)[log_(2)(\sqrt(4x))]=1?
Mathematics
2 answers:
Nadusha1986 [10]3 years ago
7 0

Answer:

No extraneous solution

Step-by-step explanation:

We have the logarithmic equation given by,

\log_{2}[\log_{2}(\sqrt{4x})]=1

i.e. \log_{2}(\sqrt{4x})=2^{1}

i.e. \sqrt{4x}=2^{2}

i.e. \sqrt{4x}=4

i.e. 4x=4^{2}

i.e. 4x=16

i.e. x=4

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 ( 0,\infty ).

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.

VikaD [51]3 years ago
3 0

The correct answer on edgen is

A) 0

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