`2^(3-x) = 565` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 25 - 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^(3-x))=ln565 `

Bring down the exponent

` (3-x)ln2=ln565`

`3-x=ln565/ln2 `

`-x=ln565/ln2-3 `

` x=-6.142`

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