Question

Testul 10,subiectul 1, exercițiul 1. Vă rog! ❤️

Answer 1

 

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

 

Answer 2

$\it log_5(4-\sqrt{11})+log_5(4+\sqrt{11}=log_5(4-\sqrt{11})(4+\sqrt{11}) =\\ \\ =log_5(16-11)=log_5 5=1$