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

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

B) $\left\{ - \frac { 1 } { 7 } \right\}$

C) $\{ - 1 \}$

D) $\left\{ - \frac { 9 } { 7 } \right\}$

Quizplus · Accepted Answer

To solve the equation $8^{x-3} = 64^{4x}$, we first express both sides of the equation in terms of a common base. Since $8 = 2^3$ and $64 = 2^6$, we can rewrite the equation as:$$(2^3)^{x-3} = (2^6)^{4x}$$Simplifying the exponents gives us:$$2^{3(x-3)} = 2^{24x}$$Since the bases are the same, we can set the exponents equal to each other:$$3(x-3) = 24x$$Expanding the left side:$$3x - 9 = 24x$$Subtracting $3x$ from both sides:$$-9 = 21x$$Dividing by 21:$$x = -\frac{9}{21} = -\frac{3}{7}$$Therefore, the solution is $x = -\frac{3}{7}$.

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

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