Question

Dau coroana si 28 de puncte.
Materie clasa a 10 a.
Multumesc anticipat.​

Answer 1

$\it log_4x=\dfrac{log_2 x}{log_2 4}=\dfrac{log_2 x}{log_2 2^2}=\dfrac{log_2x}{2}\\ \\ \\ log_8x=\dfrac{log_2 x}{log_2 8}= \dfrac{log_2 x}{log_2 2^3}=\dfrac{log_2x}{3} \\ \\ \\ Ecua\c{\it t}ia\ devine:\\ \\ log_2 x+\dfrac{log_2 x}{2}+\dfrac{log_2 x}{3}=\dfrac{11}{6}|_{\cdot6} \Rightarrow 6log_2 x+3log_2 x+2log_2 x=11 \Rightarrow\\ \\ \\ \Rightarrow 11log_2x=11|_{:11} \Rightarrow log_2 x=1 \Rightarrow x=2$

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