[tex]23^{2x-1}\ \textless \ 23^{x+8}\\
2x-1\ \textless \ x+8\\
2x-x\ \textless \ 8+1\\
x\ \textless \ 9\\
x\in \{0,1,...,8\}[/tex]
[tex]15^9\ \textgreater \ 15^{x+2}\\
9\ \textgreater \ x+2\\
x+2\ \textless \ 9\\
x\ \textless \ 9-2\\
x\ \textless \ 7\\
x \in \{0,1,2,...6\}[/tex]