Find the Value of x: Math Problem

  • Context: High School 
  • Thread starter Thread starter fku4321
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Discussion Overview

The discussion revolves around solving the equation (6^x) + 1 = (2^x) + 2 for the value of x. Participants explore various approaches to finding the solution, including numerical approximations and methods for solving equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants express the need for the problem to be categorized as homework and request that the original poster provide their attempts at solving it.
  • One participant suggests that the approximate value of x is around 0.5, referencing a comparison between √6 and √2.
  • Another participant argues that 0.48 is not the exact answer, stating that it is merely a numerical approximation and that the exact solution is irrational without a closed form.
  • A later reply mentions that a better numerical approximation is 0.4895363 and suggests using the Newton-Raphson Method for finding numerical solutions.
  • One participant expresses gratitude for the explanations provided, indicating that they found the information helpful.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact value of x, with multiple competing views on what constitutes an acceptable answer and how to approach the problem.

Contextual Notes

There is a lack of clarity regarding the definitions of "exact" and "approximate" solutions, as well as the methods available for solving the equation. Some assumptions about the nature of the solution remain unaddressed.

fku4321
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(6^x)+1=(2^x)+2
please find the value of x , thanks
 
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fku4321 said:
(6^x)+1=(2^x)+2
please find the value of x , thanks

This should really be in the homework section, but what have you tried?
 


fku4321 said:
(6^x)+1=(2^x)+2
please find the value of x , thanks

Hello.

Please show working. Thanks.
 


this isn't homework
 


about 0.5, comparing √6 to √2
 


It doesn't matter, it's a homework style question. You can add why you need it solved etc, and then maybe we'll give a bit of leeway.
 


my friend asked me this question and i solved for a whole day still can't can get the exact answer 0.48
 


The problem is that 0.48 isn't the exact answer. It's only a numerical approximation.
A better approximation is 0.4895363 but even this isn't exact. The exact answer is irrational and doesn't have a closed form solution in terms of surds and logs and whatnot.

If you just wanted to find a numerical approximation however, there are quite a few tools you can use, such as the Newton-Raphson Method.
 


thanks for your explanation ,it really helps me a lot
 
  • #10


Please report threads like this.
 

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