Boxed Equations aligned at "="

Question

trying to achieve a structured, boxed equation, which is aligned at the "=". I googled for quite a time, maybe I used the wrong keywords bur I only found equations that are centred, or only one lined, but never aligned to "=". May best solution until now is this:

\documentclass[12pt]{book}
\setlength\parindent{0pt}
\usepackage{amsmath,mathtools}
\usepackage{empheq}
\setlength\fboxsep{0.5cm}
\begin{document}

\begin{center}
\begin{empheq}[box=\fbox]{align*}
  log_{b} a \overset{!}{=} \frac{lg(a)}{lg(b)} \\
  \\
  10^x=2 \\
  x=lg(2) \\
  10^{lg(2)}=2 \\
  \\
  a^n=c \\
  10^{lg(a)}^{n}=10^{lg(c)} \\
  10^{lg(a) /cdot n}=10^{lg(c)} \\
  lg(a)/cdot n=lg(c) \\
\end{empheq}
\end{center}
\end{document}

Sadly it doesn't display the \cdot AND it gives me a double superscript error because of the "^" AND I don't know how to define that it should align all lines to the "=", like in Microsoft Word f.e.

:/

Please, if someone would be so kind to deliver a short solution for this? :) Thx

Answer 1

You don't need empheq for this. In any case, there is no need for center around empheq; it's actually wrong to add it.

If you want to align the equals sign, tell TeX to with &.

\documentclass[12pt]{book}
\usepackage{amsmath}

\setlength\fboxsep{0.5cm}

\begin{document}

\[
\boxed{\begin{aligned}
  \log_{b} a &\overset{!}{=} \frac{\lg(a)}{\lg(b)} \\
  \\
  10^x&=2 \\
  x&=\lg(2) \\
  10^{\lg(2)}&=2 \\
  \\
  a^n&=c \\
  10^{\lg(a^{n})}&=10^{\lg(c)} \\
  10^{\lg(a) \cdot n}&=10^{\lg(c)} \\
  \lg(a)\cdot n&=\lg(c)
\end{aligned}}
\]

\end{document}

Note \log and \lg; also \cdot and not /cdot. I fixed the mathematical error in line 6.

Using “lg” for the base 10 logarithm is not common. In computer science it usually denotes the base 2 logarithm.

Answer 2

• You should write \lg instead of lg
• For a double superscript, we should write {a^b}^c
• For the alignment, you have to put & before the =

Here is the code:

\documentclass[12pt]{book}
\setlength\parindent{0pt}
\usepackage{amsmath,mathtools}
\usepackage{empheq}
\setlength\fboxsep{0.5cm}

\begin{document}

\begin{center}
\begin{empheq}[box=\fbox]{align*}
  \log_{b} a & \overset{!}{=} \frac{\lg(a)}{\lg(b)} \\[1em]
  10^x& =2 \\
  x& =\lg(2) \\
  10^{\lg(2)}& =2 \\[1em]
  a^n& =c \\
  {10^{\lg(a)}}^{n} & =10^{\lg(c)} \\
  10^{\lg(a) \cdot n} & =10^{\lg(c)} \\
  \lg(a)\cdot n & =\lg(c) 
\end{empheq}
\end{center}
\end{document}

Answer 3

I guess lg denotes the \log function, and cdot, \cdots. The aligned environments (there are several) do not guess where you want to align, and you have to mark the alignment point with an ampersand. If you don't, they're by default aligned at the end of lines.

Unrelated remarks: you don't have to use the center environment for these equations, as they are centred. It only adds spurious vertical spacing to the normal spacing of equations. Also, if you load empheq, needless to load amsmath nor mathtools, as the former package already does it.

\documentclass[12pt]{book}
\setlength\parindent{0pt}
\usepackage{empheq}
\setlength\fboxsep{0.5cm}

\begin{document}

\begin{empheq}[box=\fbox]{align*}
  \log_{b} a & \overset{!}{=} \frac{\log(a)}{\log(b)} \\
  \\
  10^x & =2 \\
  x & =\log(2) \\
  10^{\log(2)} & =2 \\
  \\
  a^n & =c \\
 { 10^{\log(a)}}^{n} & =10^{\log(c)} \\
  10^{\log(a) /\cdot n} & =10^{\log(c)} \\
  \log(a)/\cdot n & =\log(c)
\end{empheq}

\end{document}