Solve the equation and express the solution in exact form.
-$$\log _ { 2 } x ^ { 2 } = \left( \log _ { 2 } x \right) ^ { 2 }$$
A) {0, 2}
B) {4}
C) {1, 2}
D) {1, 4}

Question

Quizplus · Accepted Answer

Let $y = \log_2 x$. The equation becomes $y^2 = (\log_2 x)^2$, which simplifies to $y^2 = 2y$. Solving for $y$, we get $y^2 - 2y = 0$, leading to $y(y - 2) = 0$. Thus, $y = 0$ or $y = 2$. Converting back to $x$, when $y = 0$, $x = 2^0 = 1$, and when $y = 2$, $x = 2^2 = 4$. Therefore, the solution set is $\{1, 4\}$.

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Solve the Equation and Express the Solution in Exact Form $\log _ { 2 } x ^ { 2 } = \left( \log _ { 2 } x \right) ^ { 2 }$