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 $y^2 = 2y$, which simplifies to $y^2 - 2y = 0$. Factoring gives $y(y - 2) = 0$, so $y = 0$ or $y = 2$. Substituting back, $\log_2 x = 0$ gives $x = 1$, and $\log_2 x = 2$ gives $x = 4$.

Solve the Equation and Express the Solution in Exact Form log⁡2x2=(log⁡2x)2\log _ { 2 } x ^ { 2 } = \left( \log _ { 2 } x \right) ^ { 2 }log2​x2=(log2​x)2

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