How to export a solution as a nice image instead of using snipping tool

Question

Hi so I'm trying to export an image such as the one below:

Given by the code:

\begin{align*}
    \text{Solving: } 5^{n+2}&=8:\\
    \log_5\left(5^{n+2}\right)&=\log_5(8),\\
    n+2&=\log_5\left(2^3\right),\\
    n&=3\log_5(2)-2\approx \boxed{-0.708}.\\
\end{align*}

I got that image using the snipping tool, but I was wondering if there is a good way to just generate this image as a standalone image by latex? I'm not quite sure. I'm really new to latex so any help would be appreciated! I mainly use overleaf, so if anyone knows how to do this for overleaf that would be great!

Was told to specify OS: Windows 11.

Oh and finally, just a side, if anyone has suggestions for how to better format that solution, that would be great too. I thought my align way was pretty good, but it does shift to the right a bit and look a bit weird. Any suggestions appreciated!

Answer 1

\documentclass[border=0pt,12pt]{standalone}
\usepackage{amsmath}
\begin{document}
\minipage{42mm}
Solving $5^{n+2}=8$.
\begin{align*}
\log_5\left(5^{n+2}\right)
    &=\log_5(8)\\
n+2
    &=\log_5\left(2^3\right)\\
n
    &=3\log_5(2)-2 \\
    &\approx \boxed{-0.708}
\end{align*}
\endminipage
\end{document}

If you need a border, change border=0pt to border=12pt. Here is the result. The magic number 42mm is obtained by trial and error.

Note that the red borders are intentionally added when converting the PDF output to PNG. Here is the Windows command to execute ImageMagick's convert. If you use Linux or others, you might not need magick prefix.

magick convert -compose copy -bordercolor red -border 1x1 -density 200 -alpha remove "filename.pdf" "filename.png"

Converting multipage PDF to a series of PNG images

1. You have to install ImageMagick and make sure that it has been registered to the PATH environment variable as follows:

2. Use the following LaTeX template whenever you want to create a bunch of PNG images. Save it as template.tex in a folder called xyz. The compilation will be done in the 3rd step below.

   \documentclass[border=12pt,12pt,multi,preview]{standalone}
   \usepackage{amsmath}
   \begin{document}
   \preview
   \minipage{42mm}
   Solving $5^{n+2}=8$.
   \begin{align*}
   \log_5\left(5^{n+2}\right)
       &=\log_5(8)\\
   n+2
       &=\log_5\left(2^3\right)\\
   n
       &=3\log_5(2)-2 \\
       &\approx \boxed{-0.708}
   \end{align*}
   \endminipage
   \endpreview
   \preview
   \minipage{42mm}
   In Vladimir Putin We Trust
   \begin{align}
       E &\not= mc^2 \
       pV &\not= nRT
   \end{align}
   \endminipage
   \endpreview
   \end{document}
   

3. To make our life easier, it is a good idea to create a batch file generator.bat and save it in xyz.

   echo off
   rem %1 PDF filename without extension
   rem %2 density
   rem %3 border color
   if exist "%~1.pdf" del "%~1.pdf"
   if exist "%~1.tex" pdflatex "%~1.tex"
   if exist "%~1-.png" del "%~1-.png"
   if exist "%~1.pdf" magick convert ^
   -compose copy ^
   -bordercolor %3 ^
   -border 1x1 ^
   -density %2 ^
   -alpha remove ^
   "%~1.pdf" "%~1-%%02d.png"
   for %%x in (aux out log toc nav snm) do (if exist "%~1.%%x" del "%~1.%%x")
   

4. Open terminal (by pressing Win+R, typing cmd and pressing enter), change the active directory to xyz, and type the following:

   generator.bat template 200 red
   

5. You will get a bunch of PNG images.

Answer 2

This mostly takes care of it. align* and flalign* seem to want to center the alignment point. There was an odd gap on the right which was due to an extra &. Thanks to Mico for finding it.

\documentclass[varwidth]{standalone}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\begin{aligned}
    \text{Solving: } 5^{n+2}&=8:\\
    \log_5\left(5^{n+2}\right)&=\log_5(8),\\
    n+2&=\log_5\left(2^3\right),\\
    n&=3\log_5(2)-2\approx \boxed{-0.708}.\\
\end{aligned}
\end{equation*}
\end{document}