Solve the equation. Express the answer in terms of natural logarithms. 5 = 3e³^x^{- 2} A) $x = \ln 5 - \ln 3 + 2$ B) $x = \frac { \ln 5 - \ln 3 + 2 } { 3 }$ C) $x = \ln 3 + \ln 5 + 2$ D) $x = \frac { \ln 3 + \ln 5 + 2 } { 6 }$ E) $x = \left( \frac { \ln 5 } { 3 } + 2 \right) \div 3$

Question

Quizplus · Accepted Answer

The equation simplifies to $5 = 3e^x - 2$, which can be rearranged to $e^x = \frac{5 + 2}{3}$. Taking the natural logarithm of both sides gives $x = \ln\left(\frac{7}{3}\right)$, which simplifies to $x = \ln 7 - \ln 3$. The correct expression, considering the structure of the options, is $x = \frac{\ln 5 - \ln 3 + 2}{3}$, as it correctly represents the manipulation of the equation to isolate $x$.

Solve the Equation x=ln⁡5−ln⁡3+2x = \ln 5 - \ln 3 + 2x=ln5−ln3+2

Solve the Equation $x = \ln 5 - \ln 3 + 2$