[tex]\displaystyle\bf\\\\log_5\left(4-\sqrt{11}\right)+log_5\left(4+\sqrt{11}\right)=?\\\\Folosim~formula\!:~~~log_ax+log_ay=log_axy\\\\log_5\left(4-\sqrt{11}\right)+log_5\left(4+\sqrt{11}\right)=\\\\=log_5\left(4-\sqrt{11}\right)\left(4+\sqrt{11}\right)=\\\\=log_5\left(4^2-\Big(\sqrt{11}\Big)^2\right)=\\\\=log_5\left(16-11\right)=log_5\left(5\right)=\boxed{\bf1}[/tex]
