Latex pgfplots loglogaxis scaling - latex

Question

I have loglog axis in Latex and i want to change scaling of the y-Axis like this: y-Axis should be signed with: 5*10e1, 10e2, 2*10e2 But this numbers should be shown in integer like: 50, 100, 200. The gird of the diagramm should be stay the same.
\documentclass[12pt]{scrartcl}
\usepackage[paperwidth=18cm, paperheight=12cm]{geometry}
%Digrammzeug
\usepackage{pgfplots}
\begin{document}
\thispagestyle{empty} % um die Seitenzahl zu endfernen
\newgeometry{left=0.1cm, right=0.1cm, top=0.1cm, bottom=0.1cm}
\begin{figure}
\centering
\begin{tikzpicture}
\begin{loglogaxis}[
axis x line=bottom,
axis y line=left,
ymax = 2.1*10^2,
xlabel=N (log),
ylabel=$ \mathrm{S_a} $ in MPa (log),
every axis x label/.style={
at={(ticklabel* cs:1.05)},
anchor=west,
},
every axis y label/.style={
at={(ticklabel* cs:1.05)},
anchor=south,
},
ytick={10, 100},
scale=1.6,
grid=both,
tick align=outside,
tickpos=left,
]
%Lasth 1
\node at (axis cs: 10^5.25,10^2.193) {Lasthorizont I};
%Lasth 2
\node at (axis cs: 10^6.2,10^1.955) {Lasthorizont II};
%Lasth 1 - 2 Gerade
\addplot[black, mark=square*] coordinates { (50966, 155.74) (477468, 90.16)};
%Lasth 2 - N_D Gerade
\addplot[black,no marks] coordinates { (477468, 90.16) (2.5*10^6, 60.16677272)};
%Dauerfestigkeit
\addplot[black, mark=square*, mark indices={1}] coordinates { (2.5*10^6, 60.16677272) (10^7, 60.16677272)};
\addplot[black, dotted, no marks] coordinates { (2.5*10^6, 60.16677272) (10^7.3, 60.16677272) };
\addplot[black, dashed] coordinates { (10^4, 60.16677272) (2.5*10^6, 60.16677272) };
%Beschriftung
\addplot[dashed] coordinates { (2.5*10^6, 60.16677272) (2.5*10^6, 10^1.7)};
\node at (axis cs: 10^5.4,10^1.85) {Zeitfestigkeit};
\node at (axis cs: 10^5.4,10^1.74) {Dauerfestigkeit};
\node at (axis cs: 10^6.85,10^1.73) {$ N_D=2,5\cdot10^6 $};
\node at (axis cs: 10^4.4,10^1.Cool {$ S_{aD} \approx $ 60.17};
%Lasthorizont III
\addplot[black, thick, mark=x] coordinates {(180000, 117.49)};
\node at (axis cs: 10^5.8, 10^2.07) {Lasthorizont III};
\end{loglogaxis}
\end{tikzpicture}
\end{figure}
\end{document}

Answer 1

I realize this question has been asked long ago, and belongs on tex.stackexchange.com, but for those who are looking for a solution and find this question without an answer; I've found a working solution which I will share below.
I found the answer to your question in #Jake's one and two answers.
What you're looking for (I think) is a combination of the axis environment with xmode=log and ymode=log. In order to get the axis labeled you combine it with log ticks with fixed point. This is a default pgf option which will modify both axis.
Since you're asking for only specific y-axis ticks I use this for the working example below using a new definition of a pgfplotsset. By the way, I commented the line with .Cool since I'm not familiar with this and it causes problems with me, feel free to un-comment it.
\begin{tikzpicture}
\pgfplotsset{
log x ticks with fixed point/.style={
xticklabel={
\pgfkeys{/pgf/fpu=true}
\pgfmathparse{exp(\tick)}%
\pgfmathprintnumber[fixed relative, precision=3]{\pgfmathresult}
\pgfkeys{/pgf/fpu=false}
}
},
log y ticks with fixed point/.style={
yticklabel={
\pgfkeys{/pgf/fpu=true}
\pgfmathparse{exp(\tick)}%
\pgfmathprintnumber[fixed relative, precision=3]{\pgfmathresult}
\pgfkeys{/pgf/fpu=false}
}
}
}
\begin{axis}
[xmode=log,
ymode=log,
log x ticks with fixed point,
axis x line=bottom,
axis y line=left,
ymax = 2.1*10^2,
xlabel=N (log),
ylabel=$ \mathrm{S_a} $ in MPa (log),
every axis x label/.style={
at={(ticklabel* cs:1.05)},
anchor=west,
},
every axis y label/.style={
at={(ticklabel* cs:1.05)},
anchor=south,
},
ytick={10, 100},
scale=1.6,
grid=both,
tick align=outside,
tickpos=left,
]
%Lasth 1
\node at (axis cs: 10^5.25,10^2.193) {Lasthorizont I};
%Lasth 2
\node at (axis cs: 10^6.2,10^1.955) {Lasthorizont II};
%Lasth 1 - 2 Gerade
\addplot[black, mark=square*] coordinates { (50966, 155.74) (477468, 90.16)};
%Lasth 2 - N_D Gerade
\addplot[black,no marks] coordinates { (477468, 90.16) (2.5*10^6, 60.16677272)};
%Dauerfestigkeit
\addplot[black, mark=square*, mark indices={1}] coordinates { (2.5*10^6, 60.16677272) (10^7, 60.16677272)};
\addplot[black, dotted, no marks] coordinates { (2.5*10^6, 60.16677272) (10^7.3, 60.16677272) };
\addplot[black, dashed] coordinates { (10^4, 60.16677272) (2.5*10^6, 60.16677272) };
%Beschriftung
\addplot[dashed] coordinates { (2.5*10^6, 60.16677272) (2.5*10^6, 10^1.7)};
\node at (axis cs: 10^5.4,10^1.85) {Zeitfestigkeit};
\node at (axis cs: 10^5.4,10^1.74) {Dauerfestigkeit};
\node at (axis cs: 10^6.85,10^1.73) {$ N_D=2,5\cdot10^6 $};
%\node at (axis cs: 10^4.4,10^1.Cool {$ S_{aD} \approx $ 60.17};
%Lasthorizont III
\addplot[black, thick, mark=x] coordinates {(180000, 117.49)};
\node at (axis cs: 10^5.8, 10^2.07) {Lasthorizont III};
\end{axis}
\end{tikzpicture}
This provides the following figure: