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e^{2x} - e^{x} = 15

(e^{x})^{2} - e^{x} = 15

let u = e^{x} ------------- eqn(1)

u^{2} - u - 15 = 0

solving the above quadratic equation, we have:

u = 4.4051 or u = -3.4015

since only positive values are valid, -3.4015 is ignored. Thus,

u = 4.4051

from eqn(1),

4.4051 = e^{x}

multiply both sides by ln to remove e on the right hand side

ln(4.4051) = ln(e^{x})

ln(4.4051) = x

x = 1.48

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