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frika

Note that the logarithmic function is determined for all [tex]x>0.[/tex]

Now solve the equation:

[tex]2\log_3x=4,\\ \\\log_3x^2=4,\\ \\3^{\log_3x^2}=3^4,\\ \\x^2=81,\\ \\x_1=9,\ x_2=-9.[/tex]

Since [tex]x_2=-9<0,[/tex] this is an extraneous solution.

Since [tex]x_1=9>0,[/tex] this is true solution.

Answer: correct option is D

Answer:

Hence, option D is correct.

x=9 is a true solution and x=-9 is a extraneous solution.

Step-by-step explanation:

" In mathematics, an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem "

" A true solution is a valid solution of the equation "

We are given a equation as:

[tex]2\log_{3}(x)=4\\\\log_{3}x^2=4\\\\x^2=3^4\\\\x^2=81\\\\x=9,-9[/tex]

Now as we know that the logarithmic function is not defined for negative 'x'.

Hence x= -9 is a invalid solution or we can say is a extraneous solution.

and x=9 is a true solution.

Hence, option D is correct.

x=9 is a true solution and x=-9 is a extraneous solution.

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