Use the One-to-One Property to solve the following equation for x. $2 ^ { 5 x } = 128$
A) $\frac { 128 } { 5 }$
B) $- \frac { 64 } { 5 }$
C) $\frac { 7 } { 5 }$
D) $\frac { 5 } { 7 }$
E)2

Question

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. Since $128 = 2^7$, we can write the equation as $2^{5x} = 2^7$. Setting the exponents equal to each other gives $5x = 7$, which solves to $x = \frac{7}{5}$.

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