Rewrite the Equation in Terms of Base E $$y = 2 ( 7 ) ^ { x }$$

question 265

Multiple Choice

Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three
decimal places.
- $$y = 2 ( 7 ) ^ { x }$$

• A) \(\mathrm { y } = 2 \mathrm { e } ^ { \mathrm { x } \ln 7 } , \mathrm { y } = 2 \mathrm { e } ^ { 1.946 \mathrm { x } }\)
• B) \(y = 7 e ^ { x } \ln 2 , y = 7 e ^ { 0.693 x }\)
• C) \(\mathrm { y } = 2 \mathrm { e } ^ { 7 \mathrm { x } } , \mathrm { y } = 22.718 ^ { 1.946 \mathrm { x } }\)
• D) \(\mathrm { y } = ( \ln 2 ) \mathrm { e } ^ { \mathrm { x } \ln 7 } , \mathrm { y } = 0.693 \mathrm { e } ^ { 1.946 \mathrm { x } }\)

---

Definitions:

Constitutionalism

The belief in limiting government power by law, ensuring a system of checks and balances within the state's framework to protect individuals' rights and liberties.

General Will

A concept in political philosophy, particularly associated with Jean-Jacques Rousseau, representing the collective interest or the common good that is in the best interest of society as a whole.

Natural Rights

Fundamental human rights based on universal natural law, predating and regardless of legal systems or governments, such as life, liberty, and property.

The Social Contract

A theory or model, originating during the Age of Enlightenment, that suggests an implied agreement among individuals to form a society and abide by its rules for mutual benefit.