How to make an equation more aligned?

Question

\color{blue}$1 - \text{q}^\text{n} \geq \text{P$_S$} | - 1 \\
\text{q}^\text{n} \geq  -1 + \text{P$_S$} | : (-1) \\
\text{q}^\text{n} \geq 1 - \text{P$_S$} |\, \text{ln}(...) \\
\text{n}\cdot \text{ln}(\text{q}) \geq \text{ln}(1 - \text{P$_S$}) | : \text{ln}(\text{q}) \\
\text{n} \geq \frac{\text{ln}(1 - \text{P$_S$)}}{\text{ln}(\text{q})}$

How can I make this look cleaner/more aligned?

Answer 1

I guess that you after something like this:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
[
\begin{alignedat}{2}
1 - q^n
    &   \geq P_S
        &\quad&   | - 1 \
-q^n 
    &   \geq  -1 + P_S 
        &&   |\times (-1) \
q^n 
    &   \leq 1 - P_S 
        &&   | \ln({\dots}) \
n \cdot \ln(q) 
    &   \leq \ln(1 - P_S) 
        &&   |\div \ln(q) \
n
    &   \leq \frac{\ln(1 - P_S)}{\ln(q)}
\end{alignedat}
]
\end{document}

I took a liberty and turn your math to usual way to wrote math and also correct one math error ...

Edit (1):

• Considered is @Sigure comment (thank you very much!).
• If for some reason you like to have this math evaluation in the blue color, than you can obtain this with the following changes of the above MWEČ

\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}
\begin{document}
[\color{blue}
\begin{alignedat}{2}
% rest is the same as is above MWE

Edit (2): Considered is @Mico comment (thank you very much!)

Edit (3): Considered is @Rmano comment (thank you very much!)

Answer 2

In OpTeX, you can use \eqalign macro:

$$ \Blue
\eqalign{
       1 - q^n &\ge P_S        &&& | - 1 \cr
          -q^n &\ge P_S - 1    &&& | \times (-1) \cr 
           q^n &\le 1 - P_S    &&& | \ln (\dots) \cr
  n\cdot\ln(q) &\le \ln(1-P_S) &&& | \div \ln(q) \cr
             n &\le {\ln(1-P_S \over \ln(q)} 
}
$$
\bye

The result is the same as in the Zarko's answer.

Note that OpTeX provides extended \eqalign macro, it allows more than single column of equations. The second column can be inserted after && and we use its right part of the second column of equations for the | -1 etc., hence there are three &&&. See the document OpTeX math, page 27, for more details.

Answer 3

\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}
\begin{document}
\begin{equation}
{\color{blue}
\begin{aligned}
1 - q^n      & \geq P_S | - 1                   \\
q^n          & \geq -1 + P_S|:(-1)              \\
q^n          & \geq 1 - P_S |\, \ln(\ldots)     \\
n\cdot\ln(q) & \geq \ln(1 - P_S)|:\ln(q)        \\
n            & \geq \frac{\ln(1 - P_S)}{\ln(q)}
\end{aligned}}
\end{equation}
\end{document}

Answer 4

Variables in math formulas are traditionally typeset in italics, in order to better distinguish them from text letters. So you shouldn't use all those \text commands, but just let TeX do its job.

Also \text{ln} is wrong (and I'm not talking about the symbol for the logarithmic function) and should be \ln.

Now, the “more aligned” depends on individual tastes. You might want that the main formulas are left aligned or that they're aligned with respect to the relation symbols therein.

Personally, I'd not add the indication of the operations performed in order to go from a line to the next, because they're rather elementary. Anyway, here are two ways to get what you want.

\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}
\begin{document}
[\color{blue!90!black}
\begin{alignedat}{2}
1 - q^n &   \geq P_S          &\quad&   |+(-1) \
-q^n    &   \geq  -1 + P_S    &&        |\times(-1) \
q^n     &   \leq 1 - P_S      &&        |;{\ln({\dots})} \
n\ln(q) &   \leq \ln(1 - P_S) &&        |;/!\ln(q) \
n       &   \leq \frac{\ln(1 - P_S)}{\ln(q)}
\end{alignedat}
]
\end{document}

With left alignment:

\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}
\begin{document}
[\color{blue!90!black}
\begin{alignedat}{2}
&1 - q^n \geq P_S          &\quad&   |+(-1) \
&{-q^n}  \geq  -1 + P_S    &&        |\times(-1) \
&q^n     \leq 1 - P_S      &&        |;{\ln({\dots})} \
&n\ln(q) \leq \ln(1 - P_S) &&        |;/!\ln(q) \
&n       \leq \frac{\ln(1 - P_S)}{\ln(q)}
\end{alignedat}
]
\end{document}

Actually, you should recall for the last step that q > 1, otherwise the step would be incorrect.