Solving 16•4^{-x}=4^x-6 Equation

[Petrus]

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,
$$|\pi\rangle$$

 

[Nono713]

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? :)

 

[chisigma]

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

$\chi$ $\sigma$

 

[Petrus]

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