Solve the logarithmic equation algebraically.Approximate the result to three decimal places. $9 + 2 \ln x = 4$
A) $e ^ { - 5 / 2 } \approx 1.082$
B) $e ^ { - 5 / 2 } \approx - 0.918$
C) $e ^ { - 5 / 2 } \approx - 1.918$
D) $e ^ { - 5 / 2 } \approx 0.082$
E) $e ^ { - 5 / 2 } \approx 2.082$

Question

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.​ $9 + 2 \ln x = 4$ ​
A) $e ^ { - 5 / 2 } \approx 1.082$
B) $e ^ { - 5 / 2 } \approx - 0.918$
C) $e ^ { - 5 / 2 } \approx - 1.918$
D) $e ^ { - 5 / 2 } \approx 0.082$
E) $e ^ { - 5 / 2 } \approx 2.082$

Quizplus · Accepted Answer

To solve the equation $9 + 2 \ln x = 4$, subtract 9 from both sides to get $2 \ln x = -5$. Divide by 2 to get $\ln x = -5/2$. Exponentiate both sides to solve for $x$, giving $x = e^{-5/2}$. Calculating $e^{-5/2}$ gives approximately 0.082.

Solve the Logarithmic Equation Algebraically 9+2ln⁡x=49 + 2 \ln x = 49+2lnx=4

Solve the Logarithmic Equation Algebraically $9 + 2 \ln x = 4$