Question

[25 pontos] Se responder só pra ganhar pontos eu denuncio!

A) log₀,₅ (3x - 1) ≥ log₀,₅ (2x + 3)

B) log₂ (x - 2) > 2

C) log₃ (-5x + 3) < 0

Preciso do desenvolvimento das questões, agradeço a colaboração.

Answer 1

Bom dia! 

A) log₀,₅ (3x - 1) ≥ log₀,₅ (2x + 3)

B) log₂ (x - 2) > 2

C) log₃ (-5x + 3) < 0

$A) \ log_ {0,5} (3x - 1) \geq log _{0,5} (2x + 3) \\ \\ (3x-1) \ \textgreater \ 0\qquad (2x+3) \ \textgreater \ 0 \ \\ \\ (3x-1) \geq (2x+3) \\ \\ 3x-2x \geq 3+1 \\ \\ x \geq 4\qquad \to x\in [4, +\infty)$



$B) log_2 (x - 2) \ \textgreater \ 2 \\ \\ 2^2\ \textgreater \ (x-2) \\ \\ 4\ \textgreater \ x-2 \\ \\ 4+2\ \textgreater \ x \\ \\ 6\ \textgreater \ x \qquad \to x\in (-\infty; 6)$


$C) log_3 (-5x + 3) \ \textless \ 0 \\ \\ x \in \emptyset$