Solve the Exponential Equation Algebraically $1000 e ^ { - 4 x } = 75$

question 45

Multiple Choice

Solve the exponential equation algebraically.Approximate the result to three decimal places.​ $1000 e ^ { - 4 x } = 75$ ​

• A) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 2.648\)
• B) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 1.352\)
• C) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 1.648\)
• D) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx 0.648\)
• E) \(- \frac { 1 } { 4 } \ln \frac { 3 } { 40 } \approx - 0.352\)

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Definitions:

Equatorial Ethyl

A term not typically used in standard chemical nomenclature and could refer to the placement of an ethyl group in an equatorial position on a cyclohexane ring, emphasizing its spatial orientation.

Chair Conformation

A three-dimensional geometric representation of cyclohexane molecules resembling a chair, minimizing strain.

Cyclohexane Derivative

A chemical compound derived from cyclohexane by replacing one or more of its hydrogen atoms with other atoms or groups.

Alkyl Substituents

Alkyl substituents are groups of atoms, derived from alkanes, that are attached to a molecule, replacing a hydrogen atom.