Question

Sabendo que log x Sen 18 =0,309 , log cos 18 =0,951 e log tg 18= 0,325. calcule o valor de x .

Answer 1

$log\ tg\ 18\° =\frac{log\ sen\ 18\°}{log\ cos\ 18\°}\\\\ 0,951=\frac{log\ sen\ 18\°}{0,325}\\\\ log\ sen\ 18\° = 0,951*0,325\\\\ log\ sen\ 18\°=0,309$

Mudança de base

$log\ sen\ 18\°=\frac{log\ sen\ 18\°}{log\ x}\\\\ 0,309=\frac{0,309}{log\ x}\\\\ log\ x=1\\\\ 10^1=x\\\\ \boxed{\therefore\ x=10}$