`2^(x + 1) = e^(1 - x)` Solve the exponential equation algebraically. Approximate the result to three decimal places.

loves2learn | Student

Take the ln of both sides

`ln(2^(x+1))=ln(e^(1-x)) `

Move the exponents out in front

`(x+1)ln2=(1-x)lne `

Multiply out using distributive property

`xln2+ln2=lne-xlne`

Gather the x terms on one side and the other terms on the other side

`xln2+xlne=lne-ln2 `

Factor out x

`x(ln2+lne)=lne-ln2 `

Divide both sides

`x=(lne-ln2)/(ln2+lne) `

`x=0.181 `