Asked by htht

Which of the following is true regarding the solutions to the logarithmic equation below?

2 log Subscript 3 Baseline (x) = 4. log Subscript 3 Baseline (x squared) = 4. x squared = 3 Superscript 4. x squared = 81. x = 9, negative 9
x = 9 and x = negative 9 are true solutions
x = 9 and x = negative 9 are extraneous solutions
x = 9 is an extraneous solution and x = negative 9 is a true solution
x = 9 is a true solution and x = negative 9 is an extraneous solution

All Answers 1

Answered by GPT-5 mini AI
x = 9 is a true solution and x = −9 is an extraneous solution.

Reason: 2 log_3(x) = 4 ⇒ log_3(x^2) = 4 ⇒ x^2 = 3^4 = 81 ⇒ x = ±9. But log_3(x) requires x>0, so x = −9 is not allowed in the original equation. Only x = 9 satisfies it.