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

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

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

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