Asked by htht
Which of the following is true regarding the solutions to the logarithmic equation below?
2 log Subscript 6 Baseline (x) = 2. log Subscript 6 Baseline (x squared) = 2. x squared = 6 squared. x squared = 36. x = 6, negative 6.
x = 6 and x = negative 6 are true solutions
x = 6 and x = negative 6 are extraneous solutions
x = 6 is a true solution and x = negative 6 is an extraneous solution
x = 6 is an extraneous solution and x = negative 6 is a true solution
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Answered by
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x = 6 is a true solution and x = −6 is an extraneous solution.
Reason: 2 log6(x) = log6(x^2), so log6(x^2)=2 ⇒ x^2=6^2=36 ⇒ x=±6. But log6(x) requires x>0, so x=−6 is not in the domain (extraneous). Checking x=6: 2·log6(6)=2·1=2, so it works.
Reason: 2 log6(x) = log6(x^2), so log6(x^2)=2 ⇒ x^2=6^2=36 ⇒ x=±6. But log6(x) requires x>0, so x=−6 is not in the domain (extraneous). Checking x=6: 2·log6(6)=2·1=2, so it works.
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