`6(2^(3x - 1)) - 7 = 9` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 33 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Add 7 to both sides

`6(2^(3x-1))=16 `

Divide by 6

`2^(3x-1)=8/3 `

Take the ln of both sides and bring down the exponent

`(3x-1)ln2=ln(8/3) `

Simplify,

`3x-1=ln(8/3)/ln2 `

`3x=ln(8/3)/(ln2)+1 `

`x=(ln(8/3)/ln2+1)/3 `

`x=0.805 `

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