Question

Sendo log 2 = x e log 3= y, calcule log(9√¯8) em função de x e y.

Answer 1

$log(9\sqrt{8})\\\\ log(3^2\sqrt{2^2*2})\\\\ log(3^2*2\sqrt{2})\\\\ log(3^2*2^1*2^\frac{1}{2})\\\\ log(3^2*2^\frac{3}{2})\\\\\ log\ 3^2+log\ 2^\frac{3}{2}\\\\ 2\ log\ 3+\frac{3}{2}\ log\ 2\\\\ 2*y+\frac{3}{2}*x\\\\ 2y+\frac{3x}{2}\\\\\ \boxed{log(9\sqrt{8})=\frac{4y+3x}{2}}$