For the last few days, I have been trying to replicate the following figure with TikZ (I am open to use pgfplots, but I have not been able to achieve much with pgfplots so far; therefore I am using TikZ).

The picture below shows the closest I have been able to get using TikZ. The code below the picture is a WME of the code I use to get the plot.

```
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{figure}[!htb]
\centering
\begin{tikzpicture}[domain=0.01:6.5]
\draw[->] (0,0) -- (6.5,0) node[right] {$\cdot$};
\draw[->] (0,0) -- (0,6.5) node[above] {$u(\cdot)$};
\draw[densely dotted, domain=0.2:3.3] plot (\x, 2.5+\x);
\draw[thick, smooth, samples=100, yshift=4.6cm, domain=0.01:6.5] plot ({ \x, ln(\x)});
\draw[-, thin, densely dotted] (0,2.7) -- (0.15,2.7) node[left] {$u(x)$};
\draw[-, thin, densely dotted] (0,5.8) -- (3.3,5.8) node[left] {$u(y)$};
\draw[-, thin, densely dotted] (0,4.25) -- (1.75,4.25);
\draw[-, thin, densely dotted] (0.15,0) -- (0.15,2.75);
\draw[-, thin, densely dotted] (1.75,0) -- (1.75,5.15);
\draw[-, thin, densely dotted] (3.25,0) -- (3.25,5.75);
\draw[-, thin, densely dotted] (0,5.15) -- (1.75,5.15);
\end{tikzpicture}
\end{figure}
\end{document}
```

If possible, I would like some help in making my plot look like the one in the first picture. Though solutions with TikZ are preferred, I am open to do it with pgfplots from scratch. Can Anyone help me in achieving my goal? Thank you all!

## Best Answer

You can actually do all the calculations within Ti

kZ, the same syntax`\coordinate (a) at (0.5,{ln(0.5)})`

works to set a coordinate in some specific point of the plot, in this case, it's`u(0.5)`

.There's only one tricky part which is the

`c(F,u)`

, there it's possible to use the`intersections`

library to brutally determine that coordinate, or do it with math. But to use math one must know that once TikZ computes a dimension it internally converts it into`pt`

and since the plot is being handled in`cm`

a unit conversion must be done:`1cm=28.4576pt`

and`1pt=0.03514cm`

. Now, knowing the an`y`

(`u(x)`

) value we can determine ist corresponding`x`

by doing`x=pow(e,y)`

where`y`

must be given in`cm`

.