what is the solution to the equation $e^{3x}=12$? round your answer to the nearest hundredth.\n$x =…

what is the solution to the equation $e^{3x}=12$? round your answer to the nearest hundredth.\n$x = 0.83$\n$x = 1.09$\n$x = 2.48$\n$x = 7.44$

what is the solution to the equation $e^{3x}=12$? round your answer to the nearest hundredth.\n$x = 0.83$\n$x = 1.09$\n$x = 2.48$\n$x = 7.44$

Answer

Explanation:

Step1: Take natural - log of both sides

Take the natural logarithm of both sides of the equation $e^{3x}=12$. Since $\ln(e^{a}) = a$, we have $\ln(e^{3x})=\ln(12)$. So, $3x=\ln(12)$.

Step2: Solve for x

Divide both sides of the equation $3x = \ln(12)$ by 3. Then $x=\frac{\ln(12)}{3}$. We know that $\ln(12)\approx2.4849$, so $x=\frac{2.4849}{3}\approx0.83$.

Answer:

A. $x = 0.83$