Solve the equation.
-$$\left( \frac { 1 } { 3 } \right) ^ { 6 x + 4 } = 9 ^ { x - 5 }$$
A) $\left\{ \frac { 3 } { 4 } \right\}$
B) $\left\{ \frac { 1 } { 7 } \right\}$
C) $\left\{ \frac { 7 } { 3 } \right\}$
D) $\left\{ \frac { 1 } { 8 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation, first express both sides with the same base. Since $9 = 3^2$, we can rewrite the equation as $\left( \frac { 1 } { 3 } \right) ^ { 6 x + 4 } = (3^2) ^ { x - 5 }$. Simplifying further, we get $3^{- (6x + 4)} = 3^{2(x - 5)}$. Equating the exponents gives $- (6x + 4) = 2(x - 5)$. Solving for $x$, we find $x = \frac { 3 } { 4 }$.

Solve the Equation (13)6x+4=9x−5\left( \frac { 1 } { 3 } \right) ^ { 6 x + 4 } = 9 ^ { x - 5 }(31​)6x+4=9x−5

Solve the Equation $\left( \frac { 1 } { 3 } \right) ^ { 6 x + 4 } = 9 ^ { x - 5 }$