Question

aveti idee la exercitiul 3?

Answer 1

Răspuns:

$x = \frac{1}{\sqrt[3]{2} }$

Explicație pas cu pas:

Reguli folosite:

$\log_{b}(a^c) = c\cdot\log_b(a)\\\log^n_{b}(c) = (\log_{n}(c))^n$

$\log^{2}_{2}x^3+3\log_{2}x^2 + 1 = 0\\9\log^2_2x+6\log_2(x) + 1 = 0\\ \\Fie \ t = \log_2(x)\\9t^2 + 6t + 1 = 0\\ \\(3t+1)^2 = 0 => t = -\frac{1}{3}\\ \log_2(x) = -\frac{1}{3}\\x = \frac{1}{\sqrt[3]{2} }$