Solve the equation.
-$$2 ^ { x ^ { 2 } - 3 } = 64$$
A) $\{ 3 \}$
B) $\{ \sqrt { 35 } , - \sqrt { 35 } \}$
C) $\{ 6 \}$
D) $\{ 3 , - 3 \}$

Question

Quizplus · Accepted Answer

First, recognize that $64 = 2^6$. So, the equation becomes $2^{x^2 - 3} = 2^6$. Equating the exponents gives $x^2 - 3 = 6$, which simplifies to $x^2 = 9$. Solving for $x$ yields $x = 3$ and $x = -3$, hence the correct answer is $\{3, -3\}$.

Solve the Equation 2x2−3=642 ^ { x ^ { 2 } - 3 } = 642x2−3=64

Solve the Equation $2 ^ { x ^ { 2 } - 3 } = 64$