Question

Please help and explain how to do this. thank you in advance!

Use natural logarithms to solve the equation. Round to the nearest thousandth. 3e^2x +5=27

Answer 1

We want to solve

`3e^(2x)+5=27`

Subtract 5 from each side.

`3e^(2x)=22`
Divide each side by 3.

`e^(2x)=7.3333`
Take natural logs of each side.

`2x=ln(7.3333)=1.9924`
Divide each side by 2.
x = 0.9962

Answer: x = 0.996 (nearest thousanth)