Solving 16•4^{-x}=4^x-6 Equation

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Discussion Overview

The discussion revolves around solving the equation $$16•4^{-x}=4^x-6$$. Participants explore different methods for manipulating the equation, including logarithmic and substitution techniques.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant expresses difficulty in solving the equation and mentions that taking the natural logarithm does not yield a solution.
  • Another participant suggests multiplying both sides by $$4^x$$, leading to a quadratic form and proposes substituting $$u = 4^x$$.
  • A third participant reiterates the original problem and suggests setting $$4^{x}=y$$ to solve for $$y$$ and subsequently for $$x$$ using logarithms.
  • A later reply indicates that the original poster successfully solved the equation, although the details of the solution are not provided.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single method for solving the equation, as multiple approaches are proposed and the original poster's final solution is not elaborated upon.

Contextual Notes

The discussion includes various methods for solving the equation, but does not clarify the assumptions or steps taken in the proposed solutions.

Who May Find This Useful

Individuals interested in algebraic equations, particularly those involving exponential terms, may find this discussion relevant.

Petrus
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Hello MHB,
I am stuck on this equation and don't know what to do, If i take ln it does not work, any advice?
$$16•4^{-x}=4^x-6$$

Regards,
$$|\pi\rangle$$
 
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Try multiplying both sides by $4^x$. You get:
$$16 = (4^x)^2 - 6 \cdot 4^x$$
Now substitute $u = 4^x$. What do you see? :)
 
Petrus said:
Hello MHB,
I am stuck on this equation and don't know what to do, If i take ln it does not work, any advice?
$$16•4^{-x}=4^x-6$$

Regards,
$$|\pi\rangle$$

Set $4^{x}=y$, then solve for y and finally find $x = \frac{\ln y}{\ln 4}$ ...

Kind regards

$\chi$ $\sigma$
 
Hello,
Thanks for the fast respond and help from you both!:) i succed to solve it with correct answer!:)
Regards,
$$|\pi\rangle$$
 

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