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

Textbook Question

Chapter 3, 3.4 - Problem 18 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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Since the bases are the same, set the exponents equal to each other

`x^2-3=x-2 `

`x^2-x-1=0 `

Use the quadratic formula

`x=-0.618 ` and `x=1.618 `

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