Which of the following is true regarding the solutions to the logarithmic equation below? 2log_6(x)=2 log_6(x^2)=2 x^2=6^2 x^2=36 x=6,-6 x=6 and x=-6 are true solutions x=6 and x=-6 are extraneous solutions x=6 is a true solution and x=-6 is an extraneous solution x=6 is an extraneous solution and x=-6 is a true solution

Ernesto Wagner

Ernesto Wagner

Answered question

2022-11-24

Which of the following is true regarding the solutions to the logarithmic equation below?
2 log 6 ( x ) = 2
log 6 ( x 2 ) = 2 x 2 = 6 2 x 2 = 36 x = 6 , 6
x=6 and x=-6 are true solutions
x=6 and x=-6 are extraneous solutions
x=6 is a true solution and x=-6 is an extraneous solution
x=6 is an extraneous solution and x=-6 is a true solution

Answer & Explanation

Eric Solis

Eric Solis

Beginner2022-11-25Added 4 answers

If we put x= 6 then
2 log 6 6 = 2 which satisfies the equation ( log 6 6 = 1)
But if we put x= -6 Then
2 log 6 ( 6 ) is undefined since log​​​​6​​​ (-6) is undefined
Therefore x= 6 is a true solution and x= -6 is an extraneous solution

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