Exponents & Radicals

**rn5a** · February 15th 2011, 08:16 AM

If

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

how do I find the value of

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

Thanks,

Ron

**Ackbeet** · February 15th 2011, 08:27 AM

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.

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