Question

Solve the equation below for x 200=50e^3x

Answer 1

`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=(\ln4)/(3)}\\\\x=(1)/(3)\ln4\\\\x=\ln4^(1)/(3)\\\\\boxed{x=\ln\sqrt[3]4}\\\\Used:\\\\\log_aa^n=n\\\\\log_ab^n=n\log_ab\\\\a^(1)/(n)=\sqrt[n]{a}`