3^log 81 (5x-3)=7 Решите плиз, 81 это основание логарифма

[latex]3^{log_{81}(5x-3)}=7[/latex] ОДЗ: [latex]5x-3\ \textgreater \ 0;x\ \textgreater \ 0.6[/latex] [latex]3^{log_{3^4}(5x-3)}=7[/latex] [latex]3^{ \frac{1}{4} log_{3}(5x-3)}=7[/latex] [latex](3^{ log_{3}(5x-3)})^{\frac{1}{4}}=7[/latex] [latex](5x-3)^{\frac{1}{4}}=7[/latex] [latex]5x-3=7^4[/latex] [latex]5x=2401+3[/latex] [latex]5x=2404[/latex] [latex]x=480.8 [/latex]