How to get tikzmark to work

Question

I am having difficulty getting \tikzmark to do its magic. I tried using the tikz library for \tikzmark as in the following code:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,tikzmark}
\begin{document}
By taking logarithms of both sides
\[
  t = \frac{30\cdot\ln(3/22)}{\ln(15/22)}
    \tikzmark{calculator}\approx
    156    
\]
\begin{tikzpicture}[overlay,remember picture]
    \draw[arrows=->] (calculator) ++(0,2ex) -- (calculator);
\end{tikzpicture}
\end{document}

But I get a complaint as follows:

! Package pgf Error: No shape named calculator is known.

See the pgf package documentation for explanation.
Type  H <return>  for immediate help.
 ...                                              

l.14     \draw[arrows=->] (calculator)
                                       ++(0,2ex) -- (calculator);

I tried a different approach where I didn't bother to load the tikzmark library:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}%,tikzmark}
\newcommand\tikzmark[1]{\tikz[overlay,remember picture] \node (#1) {};}
\begin{document}
By taking logarithms of both sides
\[
  t = \frac{30\cdot\ln(3/22)}{\ln(15/22)}
    \tikzmark{calculator}\approx
    156    
\]
\begin{tikzpicture}[overlay,remember picture]
    \draw[arrows=->] (calculator) ++(0,2ex) -- (calculator);
\end{tikzpicture}
\end{document}

and I get the totally cryptic error:

! Undefined control sequence.
l.2 \savepointas
                {calculator}{pgfid1}
? 

I thought I understood overlays and whatnot, but clearly I don't.

What I would like to do here is something like the following kludge:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}%,tikzmark}
\newcommand\tikzmark[1]{\tikz[overlay,remember picture] \node (#1) {};}
\begin{document}
By taking logarithms of both sides
\[
  t = \frac{30\cdot\ln(3/22)}{\ln(15/22)}
    \raisebox{-\height}{$\stackrel{\approx}{\stackrel{\uparrow}{\makebox[0pt]{use calculator}}}$}
    156    
\]
\end{document}

Answer 1

The tikzmark library uses the pic coordinate system, so you need to call the marks using the pic cs: prefix, as in (pic cs:calculator):

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,tikzmark}
\begin{document}
By taking logarithms of both sides
\[
  t = \frac{30\cdot\ln(3/22)}{\ln(15/22)}
    \tikzmark{calculator}\approx
    156    
\]
\begin{tikzpicture}[overlay,remember picture]
    \draw[arrows=->] 
    ( $ (pic cs:calculator) +(6pt,-2.5ex) $ ) -- 
    ( $ (pic cs:calculator) +(6pt,-0.5ex) $ );
    \node[anchor=north]
    at ( $ (pic cs:calculator) +(6pt,-2ex) $ )
    {Use calculator};
\end{tikzpicture}
\end{document}

With your second code, the problem is that in the first run, the coordinates for the mark mark are still not calculated. The second run of the code works since by then the coordinate has been appropriately calculated and the arrow can be drawn. You can avoid the error in the first run by using

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc}%,tikzmark}
\newcommand\tikzmark[1]{\tikz[overlay,remember picture] \node (#1) {};}
\begin{document}
By taking logarithms of both sides
\[
  t = \frac{30\cdot\ln(3/22)}{\ln(15/22)}
    \tikzmark{calculator}\approx
    156    
\]
\expandafter \ifx\csname pgf@sys@pdf@mark@pos@pgfid\the \csname
pgf@picture@serial@count\endcsname\endcsname\relax
\else
\begin{tikzpicture}[overlay,remember picture]
\draw[arrows=->] 
  ( $ (calculator) +(6pt,-2.5ex) $ ) -- 
  ( $ (calculator) +(6pt,-0.5ex) $ );
\node[anchor=north]
  at ( $ (calculator) +(6pt,-2ex) $ )
  {Use calculator};\end{tikzpicture}
\fi
\end{document}

Answer 2

For fun, a variant without tikz and without the need for an additional LaTeX run:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
By taking logarithms of both sides
\[
  t = \frac{30\cdot\ln(3/22)}{\ln(15/22)}
  \underset{\mathclap{\shortstack{$\uparrow$\\[-.2ex]use calculator}}
  }{\approx} 156
\]
\end{document}

Remarks:

• Package mathtools loads amsmath and defines further commands like \mathclap, in this case also \makebox[0pt]{...} can be used.
• \underset comes from package amsmath.
• \shortstack is defined in the LaTeX kernel.

Answer 3

A variation which just creates a coordinate underneath the \approx sign, picking up the horizontal distance from two marks and adjusting the vertical somewhat. This coordinate is then used as the basis for placing the node and arrow.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,tikzmark}
\begin{document}
By taking logarithms of both sides
\[
  t = \frac{30\cdot\ln(3/22)}{\ln(15/22)}
  \tikzmark{calculator}\approx\tikzmark{otherside}
    156
\]
\begin{tikzpicture}[overlay,remember picture]
  \coordinate (target) at ($(pic cs:calculator)!1/2!(pic cs:otherside) - (0,.5ex)$);
  \draw[arrows=->] (target) ++(0,-2ex) node [anchor=north] {use calculator} -- (target);
\end{tikzpicture}
\end{document}