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

Textbook Question

Chapter 3, 3.4 - Problem 36 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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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


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 `

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