If
$\displaystyle 2^x/(1+2^x) = 1/4$
how do I find the value of
$\displaystyle 8^x/(1+8^x)?$
Thanks,
Ron
That's a fun little problem. Try this:
$\displaystyle 2^{x}=\dfrac{1}{4}(1+2^{x})$
$\displaystyle \dfrac{3}{4}\,2^{x}=\dfrac{1}{4}$
$\displaystyle 3\cdot 2^{x}=1$
$\displaystyle 2^{x}=\dfrac{1}{3}=\left(8^{1/3}\right)^{x}.$
Raise both sides to the power 3 to obtain
$\displaystyle 8^{x}=\dfrac{1}{27}.$
Plug this into the desired expression.