Solve the equation.
-$$8 ^ { x - 3 } = 64 ^ { 4 x }$$
A) $\left\{ - \frac { 3 } { 7 } \right\}$
B) $\left\{ - \frac { 1 } { 7 } \right\}$
C) $\{ - 1 \}$
D) $\left\{ - \frac { 9 } { 7 } \right\}$

Question

Quizplus · Accepted Answer

First, express both sides of the equation in terms of a common base. Since $8 = 2^3$ and $64 = 2^6$, the equation becomes $2^{3(x-3)} = 2^{24x}$. Equating the exponents gives $3(x - 3) = 24x$, which simplifies to $3x - 9 = 24x$. Solving for $x$ yields $x = -\frac{3}{7}$.

Solve the Equation 8x−3=644x8 ^ { x - 3 } = 64 ^ { 4 x }8x−3=644x

Solve the Equation $8 ^ { x - 3 } = 64 ^ { 4 x }$