TikZ PGF – Fixing Dimension Too Large Error with exp(x) in pgfplots

Question

I hope, someone can help me. I've the following problem:

I want to draw a Graph like this

The picture shows the following graphs: exp(x), ln(x), x

my code is:

\begin{tikzpicture} 
    \draw[ultra thin,color=gray] (-0.1,-0.1) grid (5,5);
    \draw[->] (-0.2,0) -- (5.2,0) node[below] {$x$}; 
    \draw[->] (0,-0.2) -- (0,5.2) node[above] {$y$};

    \draw (0,0)--(5,5);

    \draw[color=blue, samples=150, thick, domain=0:1.6095]   
            plot (\x,{exp(\x r)}) node[right] {$f(x) = exp x$};
    \draw[color=cyan, samples=150, thick, domain=1:5]
            plot (\x,{ln(\x r)}) node[right] {$f(x) = ln x$};
\end{tikzpicture}

My LaTeX Compliler throws me the follwoing message:

plot (\x,{exp(\x r)})

node[right] {$f(x) = exp x$}; I can't work with sizes bigger than about 19 feet. Continue and I'll use the

largest value I can.

The Domain Value for exp(x) is 1.6095 because exp(1.6095) = 5

I hope, you can help me.

Answer 1

In your question title it mentions pgfplots but you don't use it. And if you don't use r(radian) indicator everything runs smoothly. I'll take the easy way out by just giving a simple pgfplots example.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture} 
\begin{axis}[xmin=-0.5,xmax=5,ymin=-0.5,ymax=5,no markers,samples=50,grid=both]
\addplot {exp(x)};
\addplot {ln(x)};
\addplot {x};
\end{axis}
\end{tikzpicture}
\end{document}

Please see the pgfplots manual for a lot more.