Use the One-to-One Property to solve the following equation for x. $\left( \frac { 1 } { 3 } \right) ^ { 8 x - 1 } = 27$
A) $\frac { 1 } { 2 }$
B) $- \frac { 1 } { 4 }$
C) $\frac { 1 } { 3 }$
D) $- \frac { 3 } { 8 }$
E) $\frac { 1 } { 8 }$

Question

Use the One-to-One Property to solve the following equation for x.​ $\left( \frac { 1 } { 3 } \right) ^ { 8 x - 1 } = 27$ ​
A) $\frac { 1 } { 2 }$
B) $- \frac { 1 } { 4 }$
C) $\frac { 1 } { 3 }$
D) $- \frac { 3 } { 8 }$
E) $\frac { 1 } { 8 }$

Quizplus · Accepted Answer

The One-to-One Property of exponential functions allows us to set the exponents equal to each other when the bases are the same. First, recognize that 27 can be written as $3^3$ and the base $\frac{1}{3}$ can be written as $3^{-1}$. Thus, the equation becomes $3^{-1(8x-1)} = 3^3$. Setting the exponents equal to each other gives $-1(8x-1) = 3$, which simplifies to $8x-1 = -3$. Solving for x, we get $8x = -2$, so $x = -\frac{1}{4}$.

Use the One-To-One Property to Solve the Following Equation for X.​

Use the One-To-One Property to Solve the Following Equation for X.