[tex]50e^{3x}=200\qquad|\text{divide both sides by 50}\\\\e^{3x}=4\qquad|\ln\ \text{both sides}\\\\\ln e^{3x}=\ln4\to3x=\ln4\qquad|\text{divide both sides by 3}\\\\\boxed{x=\dfrac{\ln4}{3}}\\\\x=\dfrac{1}{3}\ln4\\\\x=\ln4^\frac{1}{3}\\\\\boxed{x=\ln\sqrt[3]4}\\\\Used:\\\\\log_aa^n=n\\\\\log_ab^n=n\log_ab\\\\a^\frac{1}{n}=\sqrt[n]{a}[/tex]
