Question

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

Answer 1

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

Answer 2

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

Answer 3

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,\[x=3^{-1/2}=\frac{1}{\sqrt{3}}\]

Answer 4

Thanks a bunches!