Finding a solution to the equation x3^(2x+1)=9x

  • Context: Undergrad 
  • Thread starter Thread starter Mppl
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Discussion Overview

The discussion revolves around finding solutions to the equation x3^(2x+1) = 9x. Participants explore methods for identifying solutions, particularly focusing on the case where x = 0 and the implications of manipulating the equation.

Discussion Character

  • Technical explanation, Homework-related

Main Points Raised

  • One participant questions how to confirm that zero is a solution to the equation, acknowledging that substituting zero yields an equality but seeking a method to find it.
  • Another participant reformulates the equation and shows that it can be factored, leading to two potential solutions: x = 0 and x = 1/2.
  • A third participant expresses gratitude for the clarification, noting that they initially considered dividing both sides by x as a method.
  • A later reply indicates a willingness to assist further without introducing new information.

Areas of Agreement / Disagreement

Participants generally agree on the solutions presented, specifically x = 0 and x = 1/2, but the discussion does not delve into the validity of these solutions beyond their acknowledgment.

Mppl
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how can I know that zero is the solution of x3^(2x+1)=9x

I mean I know that it is the solution cause if I substitute zero I'll get an equality but how can I find it?
 
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Is this the equation you want to solve:
x3^{2x+1}=9x?
If so, x3^{2x+1}=9x\Leftrightarrow x(3^{2x+1}-9)=0\Leftrightarrow x=0\text{ or } 3^{2x+1}=3^2\Leftrightarrow 2x+1=2\Leftrightarrow x=\frac{1}{2}
 
oh thanks man, all I could think about was to divide both sides by x. Thats so simple...

Thank you very much
 
Just happy to help
 

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