Which of the following shows the extraneous solution to the logarithmic equation log7(3x^3+x)-log7(x)=2

The correct option is C, i.e., x=3 and x=-7.

Explanation:

The given equation is,

Using product property of logarithm

On comparing both sides,

Using grouping method 4x can be written as (7x-3x). Because the product of 7 and -3 is equal to the constant term -21 and the addition of 7 and -3 is equal to the coefficient of x.

Equate each factor equal to 0.

The value of x is 3 and -7. Therefore, the option C is correct.

The correct answer option is x = 4.

Step-by-step explanation:

We are given the following logarithmic equation and we are to determine whether which of the given options shows its extraneous solution:

We can rewrite it as:

But we know that

So,

Cancelling the log to get:

Further simplifying it to get:

x = 4

A)

Step-by-step explanation:

We can use logarithm properties to write it as:

On removing it gives:

Taking square root both sides.

Solving for we get:

and

Subtracting by 1 to both sides of both the above equations.

and

and

So we have got two solutions for the logarithmic equation.

Now we check the validity of the solutions by plugging values in the equation

Plugging

 [As ]

So, thats a valid solution.

Plugging

As is undefined, so is not a valid solution which means its extraneous.

B

Step-by-step explanation:

C.) x= -4

Step-by-step explanation:

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C.

Step-by-step explanation:

Given:

The given equation is

We need to determine the extraneous solution of the equation.

Solving the equation:

To determine the extraneous solution, we shall first solve the given equation.

Applying the log rule , we get;

Again applying the log rule, if then

Thus, we have;

Simplifying the equation, we get;

       

       

Factoring the equation, we get;

Thus, the solutions are

Extraneous solutions:

The extraneous solutions are the solutions that does not work in the original equation.

Now, to determine the extraneous solution, let us substitute x = 3 and x = -7 in the original equation.

Thus, we get;

     

Since, we know that is undefined.

Thus, we get;

Undefined = Undefined

This is false.

Thus, the solution x = 3 does not work in the original equation.

Hence, x = 3 is an extraneous solution.

Similarly, substituting x = -7, in the original equation. Thus, we get;

   

   

Simplifying, we get;

Undefined =

Undefined = 3.06

This is false.

Thus, the solution x = -7 does not work in the original solution.

Hence, x = -7 is an extraneous solution.

Therefore, the extraneous solutions are x = 3 and x = -7

its a

Step-by-step explanation:

Option C. x = -4

Step-by-step explanation:

We have to find the extraneous solution of the given logarithmic equation.

[Since log ()=log a - log b ]

Now

⇒

x =  ±4

Now we put x = 4 in the logarithmic equation

   So x = 4 is the real solution

Now we put x = -4 in the logarithmic equation

Since logarithm of any negative number is not defined so x = -4 will be the extraneous solution.

The answer is C. x=-4

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