`400/(1 + e^(-x)) = 350` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 42 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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`400=350(1+e^(-x)) `

`1+e^(-x)=8/7 `

`e^-x=1/7 `

Take the ln of both sides

`lne^(-x)=ln(1/7) `

Bring down the exponent

`-xlne=ln(1/7) `

Simplify

`x=1.946 `

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