Solve the equation.
-$$32 ^ { x - 1 } = 64 ^ { 3 x }$$
A) $\left\{ - \frac { 5 } { 13 } \right\}$
B) $\left\{ - \frac { 5 } { 4 } \right\}$
C) $\left\{ - \frac { 1 } { 2 } \right\}$
D) $\left\{ - \frac { 1 } { 13 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation $32^{x-1} = 64^{3x}$, we can express both sides as powers of 2, since 32 is $2^5$ and 64 is $2^6$. The equation becomes $(2^5)^{x-1} = (2^6)^{3x}$. Simplifying the exponents gives us $2^{5(x-1)} = 2^{18x}$. Setting the exponents equal to each other gives $5(x-1) = 18x$, which simplifies to $5x - 5 = 18x$. Solving for $x$ gives $x = -\frac{5}{13}$.

Solve the Equation 32x−1=643x32 ^ { x - 1 } = 64 ^ { 3 x }32x−1=643x

Solve the Equation $32 ^ { x - 1 } = 64 ^ { 3 x }$