How Do You Solve 4^x = 8x Algebraically?

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around the equation 4^x = 8x, focusing on methods to solve it algebraically. Participants explore the nature of the equation and the possibility of finding solutions through various approaches.

Discussion Character

  • Debate/contested, Exploratory, Technical explanation

Main Points Raised

  • One participant expresses difficulty in solving the equation algebraically and mentions that they found one solution, x = 2, but seeks a method to derive it.
  • Another participant questions the feasibility of solving the equation algebraically.
  • A different participant states that the equation has two real solutions that can be found graphically and notes that it is a transcendental equation, suggesting that solutions can be expressed in terms of the Lambert function.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the equation can be solved algebraically, with some asserting it cannot while others suggest graphical methods and the Lambert function as potential approaches.

Contextual Notes

The discussion highlights the transcendental nature of the equation and the implications this has for finding solutions, but does not resolve the methods or assumptions involved in solving it.

amcavoy
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Wow, I can't believe I couldn't do this.

[tex]4^x=8x[/tex]

I tried taking the natural logarithm of both sides, but that didn't help very much. I can see that an answer is 2, but I want to know how to get to that algebraicly.
 
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who says you can do it algebraically?
 
It has 2 real solutions which can be found graphically.The equation is transcendental.

The solutions are expressible in terms of the Lambert function

Daniel.
 
Last edited:
Alright well thanks for your help.
 

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