Question

1- calcule o valor de X no determinante a seguir:
(foto)

Answer 1

$\left[\begin{array}{ccc}log\ ^x_8&log\ ^x_4&log\ ^x__1_6\\1&1&1\\1&2&2\end{array}\right] = -\frac{3}{2} \\\\\\\ 2\ log\ ^x_8+2\ log\ ^x\ _1_6+log\ ^x_4 -log\ ^x\ _1_6-2log\ ^x_4-2\ log\ ^x_8 = -\frac{3}{2}\\\\\ log\ ^x_1_6-log\ ^x_4 = - \frac{3}{2}$

Agora mudamos de base os logs.

$log\ ^x\ _1_6- \frac{log\ ^x\ _1_6}{log\ ^4\ _1_6 } =- \frac{3}{2} \\\\\\\ log\ ^4\ _1_6 = x\\\\ 16^x = 4\\\\ 4^2^x =4^1\\\\ \boxed{x= \frac{1}{2} }$

$log\ ^x\ _1_6- \frac{log\ ^x\ _1_6}{ \frac{1}{2} } =- \frac{3}{2}\\\\ log\ ^x\ _1_6- 2\ log\ ^x\ _1_6 =- \frac{3}{2}$

$-\ log\ ^x\ _1_6 =- \frac{3}{2}\\\\ \ log\ ^x\ _1_6 =\frac{3}{2}\\\\ 16 ^\frac{3}{2} = x\\\\ 4^ \frac{6}{2} = x\\\\ 4^3=x\\\\ \boxed{x=64}$