Give the answer in exact form.
-$$3 ^ { 2 x } - 3 \left( 3 ^ { x } \right) = 40$$
A) $\left\{ \log _ { 3 } 8 \right\}$
B) $\{ 3 \ln 8,3 \ln ( - 5 ) \}$
C) $\left\{ \log _ { 3 } 8 , \log _ { 3 } ( - 5 ) \right\}$
D) $\{ 3 \ln 8 \}$

Question

Quizplus · Accepted Answer

The equation can be rewritten as a quadratic equation in terms of $3^x$. Let $y = 3^x$, then the equation becomes $y^2 - 3y - 40 = 0$. Factoring this equation gives $(y - 8)(y + 5) = 0$, so $y = 8$ or $y = -5$. Since $y = 3^x$, and $3^x$ cannot be negative, we discard $y = -5$. Therefore, $3^x = 8$, and solving for $x$ gives $x = \log_3 8$.

Give the Answer in Exact Form 32x−3(3x)=403 ^ { 2 x } - 3 \left( 3 ^ { x } \right) = 4032x−3(3x)=40

Give the Answer in Exact Form $3 ^ { 2 x } - 3 \left( 3 ^ { x } \right) = 40$