`e^(3x) = 12` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 29 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

Posted on

Take the ln of both sides

`lne^(3x)=ln12 `

Bring down the exponent

`3xlne=ln12 `

Simplify,

`x=0.828 `

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loves2learn | (Level 3) Salutatorian

Posted on

To solve equations, you need to isolate the variable.

Use a ln because you can use its' properties to bring down the x so you can solve for it.

Given,

Then

and

Therefore,

`lne^3x=ln12 `

`3xlne=ln12 `

, so this simplifies to,

`3x=ln12 `

Divide both sides by 3 (you need to do the same thing on all sides) and simplify,

`x=0.828 `

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