`e^(2x) - 5e^x + 6 = 0` Solve the exponential equation algebraically. Approximate the result to three decimal places.

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balajia | College Teacher | (Level 1) eNoter

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`(e^x)^2-5e^x+6=0`

Put `e^x=t`

`t^2-5t+6=0`

`t^2-3t-2t+6=0`

`t(t-3)-2(t-3)=0`

`(t-2)(t-3)=0`

`t=2 and t=3`

`e^x=2 and e^x=3.`

`x=ln2 and x=ln3.`

`x=0.693 and x=1.099`