Question

Logaritmo ,dúvida.Como resolvo essa duas equações?
2log2(x+1)=3
log2[log3(x-1)]=2
agradeço desde já pela ajuda!

Answer 1

$2log_2(x+1)=3\\\\ log_2(x+1)^2=3\\\\ 2^3=(x+1)^2\\\\ 8 = (x+1)^2\\\\ (x+1)=\sqrt{8}\\\\ (x+1)=2\sqrt{2}\\\\ \boxed{x=2\sqrt{2}-1}$

$log_2[log_3(x-1)]=2\\\\\ 2^2=log_3(x-1)\\\\ 4=log_3(x-1)\\\\ 3^4=x-1\\\\ x-1=81\\\\ \boxed{x=82}$