Question

(log de x na base 2) elevado ao quadrado menos 9 vezes log de x na base 8 igual a 4

Answer 1

$x > 0\\(log\frac{x}{2})^2 - 9log\frac{x}{8} = 4\\(log\frac{x}{2}})^2 - log\frac{x^9}{8} = 4\\(log\frac{x}{2}})^2 - \frac{log\frac{x^9}{2}}{log\frac{8}{2} } = 4\\(log\frac{x}{2}})^2 - log\frac{x^9}{2}/3 = 4\\ (log\frac{x}{2}})^2 - 9log\frac{x}{2}/3 = 4\\(log\frac{x}{2}})^2 - 3log\frac{x}{2} = 4\\ t = (log\frac{x}{2}})\\t^2 - 3t = 4\\t = -1\\t = 4\\log\frac{x}{2} = 4\\ x' = 16\\log\frac{x}{2}  = -1\\x'' = 1/2$