Solve the equation.
-$$4 ^ { x - 3 } = 32 ^ { 4 x }$$
A) $\left\{ - \frac { 1 } { 3 } \right\}$
B) $\left\{ - \frac { 1 } { 6 } \right\}$
C) $\{ - 1 \}$
D) $\left\{ - \frac { 6 } { 7 } \right\}$

Question

Quizplus · Accepted Answer

First, express both sides of the equation in terms of a common base. Since $32 = 2^5$, we can rewrite the equation as $2^{2(x-3)} = (2^5)^{4x}$. Simplifying both sides gives $2^{2x-6} = 2^{20x}$. Setting the exponents equal to each other, $2x - 6 = 20x$, solving for $x$ gives $x = -\frac{1}{3}$.

Solve the Equation 4x−3=324x4 ^ { x - 3 } = 32 ^ { 4 x }4x−3=324x

Solve the Equation $4 ^ { x - 3 } = 32 ^ { 4 x }$