## anonymous 5 years ago Solve for . Please round the answer to four decimal places. 2^(4/log[3]x)=1/256 Steps would be appreciated.

1. anonymous

$2^{4/\log_{3}x }=1/256$

2. anonymous

First consider the fact that 256 = 2^8. Then$2^{4/\log_3x}=1/2^8=2^{-8}$

3. anonymous

This statement is true only if the exponents are equal. So,$\frac{4}{\log_3{x}}=-8$Rearranging,$\log_3{x}=-\frac{1}{2}$By the definition of logarithm, this is equivalent to,$x=3^{-1/2}=\frac{1}{\sqrt{3}}$

4. anonymous

Thanks a bunches!