MHB Solving 16•4^{-x}=4^x-6 Equation

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The equation 16•4^{-x}=4^x-6 can be simplified by multiplying both sides by 4^x, resulting in 16 = (4^x)^2 - 6•4^x. Substituting u = 4^x allows for easier manipulation of the equation. By setting 4^x = y, the equation can be solved for y, leading to the final solution for x as x = ln(y)/ln(4). The original poster successfully solved the equation with the provided guidance.
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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