0;\ \ 5x>2;\ \ x>\frac25;\ \ x\in\left(\frac25;+\infty\right);\\
5x-2=8;\\
5x=6;\\
x=\frac65\in\left(\frac25;+\infty\right);\\
" alt="17^{\log_{17}\left(5x-2\right)}=8;\\
5x-2>0;\ \ 5x>2;\ \ x>\frac25;\ \ x\in\left(\frac25;+\infty\right);\\
5x-2=8;\\
5x=6;\\
x=\frac65\in\left(\frac25;+\infty\right);\\
" align="absmiddle" class="latex-formula">
Ответ: