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"Solve the following:

e^(2x+1)+2e^(x+2)-3=0"

Can you show me tbe steps coz I have tried to solve it for dozens of times but failed.

Looking at the equation, you can see how it kind of looks like a polynomial. In fact, it can be cleaned up a little using the algebra of exponents, i.e.,

e^(a+b) = (e^a)(e^b) and (e^x)^c = e^(cx)

so that it looks like

e^(2x+1) + 2e^(x+2) - 3 = 0 --> {(e^x)^2}(e^1) + 2(e^x)(e^2) - 3 = 0 --> ay^2 + by - 3 = 0

where y = e^x and a = e and b = 2e^2. You can then use the quadratic formula to solve for y and then get x = ln(y). Note that y must be > 0 or else this doesn't work (plugging in the numbers it looks like y > 0, so you're OK).

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