Question

Помогите плиз, ребята

Answer 1

1)
$log_5 (2x-5)=2 \ log_5 (2x-5)=log_5 25 \\ 2x-5=25 \\ 2x=30 \\ x=15$

2)
$lg (x-3)+lg 3 = lg 4 \\ 3(x-3)=4 \\ 3x-9=4 \\ 3x=13 \\ x=4 frac{1}{3}$

3)
$log_{frac{1}{2}} (2x-8) textgreater -1 \\ 2x-8 textgreater 0; x textgreater 4\\ log_{frac{1}{2}} (2x-8) textgreater log_{frac{1}{2}} 2 \\ 2x-8 textless 2 \\ 2x textless 10 \\ x textless 5 \\ xin(4;5)$

4)
$log_4 (2x-4) textless 1 \\ 2x-4 textgreater 0; x textgreater 2 \\ log_4 (2x-4) textless log_4 4 \\ 2x-4 textless 4 \\ 2x textless 8 \\ x textless 4 \\ xin(2;4)$

5)
$log_5 75 -log_5 3 = log_5 frac{75}{3}=log_5 25 = 2$

6)
$sqrt{4x+5} =5 \\ 4x+5 geq 0; x geq -1.25 \\ 4x+5=25 \\ 4x=20 \\ x=5$