- #1
whysoserious
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Homework Statement
4^x = x^4. My instructor wants me to find the answer that is -0.77, not 2 or 4. And showing work as well.
Solve 4^x = x^4: -0.77 Answer w/Work
- Thread starter whysoserious
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Homework Help Overview
The problem involves solving the equation 4^x = x^4, with a specific focus on finding the solution at x = -0.77. The original poster notes that their instructor requires this particular solution and emphasizes the need to show work.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants suggest various methods, including graphing the functions to find their intersection points and using logarithmic transformations. There is mention of the Lambert's W function as a potential approach, though it is noted that no elementary function can solve the equation directly. Some participants express frustration over being overlooked in the discussion.
Discussion Status
The discussion is ongoing, with multiple approaches being explored, including graphical methods and numerical solutions. Participants are actively engaging with each other's suggestions, though there is no explicit consensus on the best method to proceed.
Contextual Notes
There is an emphasis on the requirement to find a specific solution of -0.77, which may influence the methods discussed. Some participants express challenges with the mathematical transformations involved, particularly with logarithmic equations.
4^x = x^4. My instructor wants me to find the answer that is -0.77, not 2 or 4. And showing work as well.
- #2
Immutef
- 11
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Did you try graphing the equations and finding where they intercept?
Last edited:
- #3
HallsofIvy
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There is no "formula" or elementary function that will solve that. I would try to get it into a form in which I could use Lambert's W function- it is defined as the inverse of [itex]xe^x[/itex].
- #4
Axiom17
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If you detail you calculations so far perhaps then can advice with this 
- #5
whysoserious
- 2
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I tried using log but I keep getting stuck at xlog2=2logx
- #6
Axiom17
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Make a quick sketch of the two functions. Just use the range [itex]-2 \leq x \leq 2[/itex] and plot the two lines together. From the graph you should be able to see the intersect and hence the answer you require.
- #7
HallsofIvy
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Why are you ignoring my post? That equation cannot be solved using elementary functions. Do a numerical solution, or graph as Axiom17 and Immutef have suggested, or use Lambert's W function.whysoserious said:
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