If \(\int\frac{2^x}{\sqrt{1-4^x}}dx=k\sin^{-1}(2^x)+c\) then \(k=\)

\(\frac{1}{2}\log 2\) \(\log 2\) \(\frac{1}{\log 2}\) \(-\frac{1}{2}\log 2\)

\(\frac{1}{\log 2}\)

Put \(2^x=t\)