# Solving for x in equation (e^2x)-(3e^x)+2=0

• theRukus
In summary, the equation (e^2x)-(3e^x)+2=0 is a mathematical expression involving x and the constant e, with various real-world applications. The first step in solving for x is to factor out the common term e^x, and the solutions for x can be found by setting each factor equal to 0. To check the solution, you can substitute it back into the original equation. Other methods for solving this equation include using the quadratic formula or graphing, but factoring and setting each factor equal to 0 is the most efficient method.
theRukus

Solve for x.
e2x-3ex+2=0

## The Attempt at a Solution

e2x-3ex+2=0
-e2x+3ex=2
ex(3-ex)=2
lnex(3-ex)=ln2
x(3-ex)=ln2

..not very sure where to go here. Any direction would be appreciated! Thanks

I wouldn't do what you wrote above. Start with this: let w = ex. Then rewrite the equation in terms of w. Does the equation look familiar now?

## What is the equation (e^2x)-(3e^x)+2=0 and why is it important?

The equation (e^2x)-(3e^x)+2=0 is a mathematical expression that involves the variable x and the mathematical constant e (approximately equal to 2.71828). It is important because it represents a specific problem that needs to be solved, and its solution can have real-world applications in various fields such as finance, physics, and engineering.

## What is the first step in solving for x in this equation?

The first step in solving for x in this equation is to factor out the common term e^x. This can be done by rewriting the equation as e^x(e^x-3)+2=0. This step is important because it simplifies the equation and makes it easier to solve for x.

## What are the possible solutions for x in this equation?

The solutions for x in this equation can be found by setting each factor equal to 0 and solving for x. So, e^x=0 and e^x-3=0. Since e^x is always positive, the only solution is e^x-3=0, which gives us x=ln(3) (where ln is the natural logarithm).

## How can I check if my solution for x is correct?

You can check if your solution for x is correct by substituting it back into the original equation. If the resulting expression is equal to 0, then your solution is correct. For example, if x=ln(3), then (e^2ln(3))-(3e^ln(3))+2=0. Simplifying this expression gives us 9-9+2=0, which is true.

## Are there any other methods for solving this equation?

Yes, there are other methods for solving this equation, such as using the quadratic formula or graphing the equation and finding the x-intercepts. However, factoring and setting each factor equal to 0 is the most efficient and straightforward method for solving this specific equation.

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