`e^(2x) - 4e^x - 5 = 0` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 39 - Precalculus (3rd Edition, Ron Larson).
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balajia | College Teacher | (Level 1) eNoter

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`(e^x)^2-4e^x-5=0`

Put `e^x=t.`

`t^2-4t-5=0`

`t^2-5t+t-5=0`

`t(t-5)+1(t-5)=0`

`(t-5)(t+1)=0`

`t=5 or t=-1`

`e^x = 5 and e^xgt0`

Take ln on both sides, we get 

`x=ln5`

`x=1.609`

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