[tex]\displaystyle\bf\\log_5(x+1)=2\\\\x+1=5^2\\\\x+1=25\\\\x=25-1\\\\\boxed{\bf x=24}\\\\Verificare\!:\\\\log_5(x+1)=log_5(24+1)=log_5(25)=log_5(5^2)=2~~~(corect)[/tex]