Use the One-to-One Property to solve the following equation for x. $$2 ^ { 3 x } = 128$$
A) $$\frac { 7 } { 3 }$$
B) $$\frac { 3 } { 7 }$$
C) $\frac { 128 } { 3 }$
D)2
E) $- \frac { 64 } { 3 }$

Question

Use the One-to-One Property to solve the following equation for x. $$2 ^ { 3 x } = 128$$ ​
A) $$\frac { 7 } { 3 }$$
B) $$\frac { 3 } { 7 }$$
C) $\frac { 128 } { 3 }$
D)2
E) $- \frac { 64 } { 3 }$

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 set $3x = 7$, solving for $x$ gives $x = \frac{7}{3}$.

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