# PGFPlots logarithmic scaling of x axis and ticks base 2

I'm trying to create a plot, where my x axis is scaled to base 2 and the ticks should be at the exact height of the coordinates. I have the logarithmic x axis, but i just can't get the ticks to be at the position of the coordinates. Also the ticks should be in the form of 2^14,2^15,... instead of 0.1*10^6 and so. Currently my plot is made by this code:

\begin{figure}[h]
\begin{tikzpicture}
\begin{axis}[xlabel=n,ylabel=used time in ms,xmode=log]
\addplot coordinates{ (2^14, 8) (2^15, 26) (2^16, 72) (2^17, 185) (2^18, 414) (2^19,956) (2^20,2017) };
\addplot coordinates{ (2^14, 9) (2^15, 28) (2^16, 73) (2^17, 195) (2^18, 441) (2^19,1032) (2^20,2155) };
\addplot coordinates{ (2^14, 8) (2^15, 23) (2^16, 65) (2^17, 175) (2^18, 406) (2^19,937) (2^20,2189) };
\addplot coordinates{ (2^14, 10) (2^15, 30) (2^16, 83) (2^17, 229) (2^18, 536) (2^19,1216) (2^20,2669) };
\addplot coordinates{ (2^14, 8) (2^15, 24) (2^16, 64) (2^17, 177) (2^18, 412) (2^19,960) (2^20,2045) };
\end{axis}
\end{tikzpicture}
\end{figure}


Currently, it looks like below picture. But it should look like this, but with 2^14,2^15,.. instead of 14,15,... . I made this plot by just leaving out the base in my coordinates. Welcome to TeX-SE! Are you looking for log basis x=2?

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\begin{document}
\begin{tikzpicture}
\begin{axis}[xlabel=$n$,ylabel=used time in ms,xmode=log,log basis x=2]
\addplot coordinates{ (2^14, 8) (2^15, 26) (2^16, 72) (2^17, 185) (2^18, 414) (2^19,956) (2^20,2017) };
\addplot coordinates{ (2^14, 9) (2^15, 28) (2^16, 73) (2^17, 195) (2^18, 441) (2^19,1032) (2^20,2155) };
\addplot coordinates{ (2^14, 8) (2^15, 23) (2^16, 65) (2^17, 175) (2^18, 406) (2^19,937) (2^20,2189) };
\addplot coordinates{ (2^14, 10) (2^15, 30) (2^16, 83) (2^17, 229) (2^18, 536) (2^19,1216) (2^20,2669) };
\addplot coordinates{ (2^14, 8) (2^15, 24) (2^16, 64) (2^17, 177) (2^18, 412) (2^19,960) (2^20,2045) };
\end{axis}
\end{tikzpicture}
\end{document} 