`500/(100 - e^(x/2)) = 20` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 41 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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`500=20(100-e^(x/2))`  

`100-e^(x/2)=25 `

`-e^(x/2)=-75 `

`e^(x/2)=75 `

Take the ln of both sides and bring down the exponent

`(x/2)lne=ln75 `

Simplify,

`x=8.635 `

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