Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4
decimal places if necessary.
-$$3 ^ { x ^ { 2 } - 7 } = 9$$
A) $\{ 3 \}$
B){ }
C) $\{ 3 , - 3 \}$
D) $\{ - 3 \}$

Question

Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4
decimal places if necessary.
-$$3 ^ { x ^ { 2 } - 7 } = 9$$
A) $\{ 3 \}$
B){   }
C) $\{ 3 , - 3 \}$
D) $\{ - 3 \}$

Quizplus · Accepted Answer

Given $3^{x^2 - 7} = 9$, we can rewrite 9 as $3^2$. Thus, the equation becomes $3^{x^2 - 7} = 3^2$. Equating the exponents gives $x^2 - 7 = 2$. Solving for $x^2$ gives $x^2 = 9$, which leads to $x = 3$ or $x = -3$. Therefore, the solution set is $\{3, -3\}$.

Solve the Equation 3x2−7=93 ^ { x ^ { 2 } - 7 } = 93x2−7=9

Solve the Equation $3 ^ { x ^ { 2 } - 7 } = 9$