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Question
"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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#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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