# Exponents & Radicals

• Feb 15th 2011, 09:16 AM
rn5a
If

$2^x/(1+2^x) = 1/4$

how do I find the value of

$8^x/(1+8^x)?$

Thanks,

Ron
• Feb 15th 2011, 09:27 AM
Ackbeet
That's a fun little problem. Try this:

$2^{x}=\dfrac{1}{4}(1+2^{x})$

$\dfrac{3}{4}\,2^{x}=\dfrac{1}{4}$

$3\cdot 2^{x}=1$

$2^{x}=\dfrac{1}{3}=\left(8^{1/3}\right)^{x}.$

Raise both sides to the power 3 to obtain

$8^{x}=\dfrac{1}{27}.$

Plug this into the desired expression.