2.
ОДЗ: 3x-10>0
3x>10
x>10/3
x>3 ¹/₃
3x-10≤(¹/₂)⁻²
3x-10≤=2²
3x≤4+10
3x≤14
x≤¹⁴/₃
x≤4 ²/₃
С учетом ОДЗ:
{x>3 ¹/₃
{x≤4 ²/₃
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
------- 3 ¹/₃ -------------- 4 ²/₃ --------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(3 ¹/₃; 4 ²/₃]
Ответ: (3 ¹/₃; 4 ²/₃]
3.
49ˣ - 8*7ˣ= -7
7²ˣ - 8*7ˣ +7 =0
y=7ˣ
y² -8y+7=0
D=64-28=36
y₁=(8-6)/2=1
y₂=(8+6)/2=7
При y=1
7ˣ =1
x=0
При у=7
7ˣ =7
х=1
Ответ: 0; 1.