As you cannot use align*
inside \[....\]
you probably want to use an array
environment, so that your code will look something like this:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[A = B * \log\frac{C}{D}, \qquad
\text{ where } \begin{array}{ll}
C &= \text{lorem} \\
D &= \text{ipsum}
\end{array}
\]
\end{document}
This produces:

Personally, I would omit the *
and write A = B\log\frac{C}{D}
. In particular, I have used:
\log
instead of \text{log}
A
instead of \text{A}
(since A
is part of the mathematics, not the text)
\qquad
to put some space between the equation and where
and that it is normally better to put the alignment character &
before the equal signs rather than before the whole equation.
Another option would be to use a cases
environment:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[A = B * \log\frac{C}{D}, \qquad
\text{ where } \begin{cases}
C = \text{lorem} \\
D = \text{ipsum}
\end{cases}
\]
\end{document}
to give

As Bernard pointed out in the comments, it is better not to use alignment in the cases environment.
Finally, when asking questions it is better to give a full minimal working example. A MWE should start with a \documentclass
command, have a minimal preamble and then \begin{document}...\end{document}
. The code should compile and be as small as possible to demonstrate your problem. Adding a MWE clarifies your question and makes it much easier for people to help you.