## anonymous 4 years ago 2^{4/l \log_{2}x}=1/256

1. anonymous

2^{4/l \log_{2}x}=1/256

2. anonymous

$2^{4\log_{2}(x)}=\frac{1}{256}$

3. anonymous

yes, how do i solve it?

4. anonymous

5. anonymous

i didn't, i just tried to interpret what you wrote

6. anonymous

yes, so can you help me solve it?

7. anonymous

we have lots of choices here

8. anonymous

okay

9. anonymous

so what are they

10. anonymous

$256=2^8$ so $\frac{1}{256}=2^{-8}$ so you could start with $2^{4\log_{2}(x)}=2^{-8}$ then $4\log_2(x)=-8$then $\log_2(x)=-2$ and so $x=2^{-2}=\frac{1}{2^2}=\frac{1}{4}$

11. anonymous

so it's .2500?

12. anonymous

or we could say $2^{4\log_{2}(x)}=\frac{1}{256}$ $2^{\log_{2}(x^4)}=\frac{1}{256}$ $x^4=\frac{1}{256}$ $x=\frac{1}{\sqrt[4]{256}}=\frac{1}{4}$ so

13. anonymous

they computer wouldnt accept the answer :(