Solve the equation.
-$( 8 ) x + 1 = \left( \frac { 2 } { 4 } \right) ^ { x - 1 }$
A) $\left\{ - \frac { 1 } { 2 } \right\}$

B) $\{ - 1 \}$

C) $\left\{ \frac { 1 } { 2 } \right\}$

D) $\left\{ - \frac { 1 } { 4 } \right\}$

Question

Solve the equation.
-$( 8 ) x + 1 = \left( \frac { 2 } { 4 } \right) ^ { x - 1 }$
A) $\left\{ - \frac { 1 } { 2 } \right\}$

B) $\{ - 1 \}$

C) $\left\{ \frac { 1 } { 2 } \right\}$

D) $\left\{ - \frac { 1 } { 4 } \right\}$

Quizplus · Accepted Answer

The equation simplifies to $8x + 1 = 2^{2(x-1)}$, which can be rewritten as $8x + 1 = 2^{2x-2}$. Recognizing that $8 = 2^3$, we can rewrite the equation as $2^{3x} + 1 = 2^{2x-2}$. Setting the exponents equal to each other because the bases are the same, we get $3x = 2x - 2$, which simplifies to $x = -2$. However, there was a mistake in my simplification process; the correct approach involves recognizing that the equation cannot be directly simplified to match the bases due to the initial setup. Instead, solving it requires a different method, such as logarithms or substitution, which was not correctly applied here. The correct answer involves recognizing that $2^{2(x-1)}$ simplifies to $2^{2x-2}$, and comparing this to $8x + 1$ does not directly lead to a simple exponent comparison due to the "+1" on the left side. My explanation incorrectly simplified the equation. Correctly solving the equation involves recognizing that $8x + 1 = (2/4)^{x-1}$ simplifies to $8x + 1 = (1/2)^{x-1}$, and finding the value of $x$ that satisfies this equation requires a method not correctly described in my initial explanation.

Solve the Equation (8)x+1=(24)x−1( 8 ) x + 1 = \left( \frac { 2 } { 4 } \right) ^ { x - 1 }(8)x+1=(42​)x−1

Solve the Equation $( 8 ) x + 1 = \left( \frac { 2 } { 4 } \right) ^ { x - 1 }$