How to solve: 2e^(x-2) = e^(x) + 7

I know that the answer is no solution but how?
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2 Answers

2e^x/e^2 = e^x + 7

2e^x = e^x(e^2) +7e^2

2e^x - e^x e^2 = 7e^2

e^x ( 2- e^2) = 7e^2

e^x = 7e^2/(2- e^2)

ln(7e^2/(2 - e^2))

which is an imaginary number so no solution
by
2e^7t +10 =16
by

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