Question

log3 (5+4*log3 (x-1))=2

Answer 1

$log_3 (5+4*log_3 (x-1))=2;\ (5+4*log_3 (x-1))=3^2;\(5+4*log_3 (x-1))=9;\ 4*log_3 (x-1)=9-5;\4*log_3 (x-1)=4;\log_3 (x-1)=4:4;\log_3 (x-1)=1;\ x-1=3^1; x-1=3; x=3+1; x=4$

проверка

$<var>log_3 (5+4*log_3 (4-1))=<var>log_3 (5+4*log_3 3)=<var><var>log_3 (5+4*1)=log_3 9=log_3 3^2=2$

а значит х=4- решение

ответ: 4