Solve the equation.
-$$\left( \frac { 1 } { 3 } \right) ^ { 4 x + 5 } = 9 ^ { x - 2 }$$
A) $\left\{ - \frac { 1 } { 6 } \right\}$
B) $\left\{ \frac { 9 } { 4 } \right\}$
C) $\left\{ - \frac { 1 } { 2 } \right\}$
D) $\left\{ - \frac { 3 } { 5 } \right\}$

Question

Quizplus · Accepted Answer

First, express both sides of the equation in terms of a common base. Since $9 = 3^2$, we can rewrite the equation as $\left( \frac { 1 } { 3 } \right) ^ { 4 x + 5 } = (3^2) ^ { x - 2 }$. Simplifying further, we get $3^{- (4x + 5)} = 3^{2(x - 2)}$. Equating the exponents gives $- (4x + 5) = 2(x - 2)$. Solving this equation for $x$ yields $x = - \frac { 1 } { 6 }$.

Solve the Equation (13)4x+5=9x−2\left( \frac { 1 } { 3 } \right) ^ { 4 x + 5 } = 9 ^ { x - 2 }(31​)4x+5=9x−2

Solve the Equation $\left( \frac { 1 } { 3 } \right) ^ { 4 x + 5 } = 9 ^ { x - 2 }$