74
QuizMultiple Choice

N/A — Exam

Question 74 • Algebra II

Which of the following is true regarding the solutions to the logarithmic equation? 2 log sub 3 x is equal to 4 log sub 3 of open paren x squared close paren is equal to 4 x squared is equal to 3 to the 4th power x squared is equal to 81 x is equal to 9 comma negative 9

Answer
A
x is equal to 9 and x is equal to negative 9 are true solutions
B
x is equal to 9 and x is equal to negative 9 are extraneous solutions
C
x is equal to 9 is an extraneous solution and x is equal to negative 9 is a true solution
D
x is equal to 9 is a true solution and x is equal to negative 9 is an extraneous solution

Explanation

The logarithm log_3 x is defined only when its argument x is positive. Thus, even if solving the equation leads to x² = 81 and the candidates x = 9 and x = −9, only x = 9 is in the original equation’s domain. So x = 9 is a true solution, while x = −9 is extraneous.

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