`8(4^(6 - 2x)) + 13 = 41` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 34 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Subtract 13 from both sides

`8(4^(6-2x))=28 `

Divide by 8

`4^(6-2x)=7/2 `

Take the ln of both sides and bring down the exponent

`(6-2x)ln4=ln(7/2) `

Simplify,

`6-2x=ln(7/2)/ln4 `

`-2x=ln(7/2)/ln4-6 `

`x=(ln(7/2)/(ln4)-6)/-2 `

`x=2.548 `

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