We want to solve
[tex]3e^{2x}+5=27[/tex]
Subtract 5 from each side.
[tex]3e^{2x}=22[/tex]
Divide each side by 3.
[tex]e^{2x}=7.3333[/tex]
Take natural logs of each side.
[tex]2x=ln(7.3333)=1.9924[/tex]
Divide each side by 2.
x = 0.9962
Answer: x = 0.996 (nearest thousanth)
