Question

Алгебра. Даю 10 баллов. Решить 5-8. С подробным объяснением.

Answer 1

$5) \ \log_{5} (2x-7)<3\\\\ODZ:2x-7>0 \ \Rightarrow \ \boxed{x>3,5}\\\\\\2x-7<5^{3}\\\\2x-7<125\\\\2x<132\\\\x<66\\\\Otvet:\boxed{x\in(3,5 \ ; \ 66)}\\\\\\6) \ \log_{0,3} (6-x)>-1\\\\ODZ:6-x>0 \ \Rightarrow \ \boxed{x<6}\\\\\\6-x<0,3^{-1}\\\\6-x<3\dfrac{1}{3} \\\\-x<-2\dfrac{2}{3} \\\\x>2\dfrac{2}{3} \\\\Otvet:\boxed{x\in\Big(2\dfrac{2}{3} \ ; \ 6\Big)}$

$7) \ \log_{0,7} (3x-5)<\log_{0,7}(x+1)\\\\ODZ:\\\\\displaystyle\left \{ {{3x-5>0} \atop {x+1>0}} \right. \\\\\\\displaystyle\left \{ {{x>1\dfrac{2}{3} } \atop {x>-1}} \right. \ \Rightarrow \ x>1\dfrac{2}{3} \\\\\\3x-5>x+1\\\\3x-x>1+5\\\\2x>6\\\\x>3\\\\Otvet:\boxed{x\in(3 \ ; \ +\infty)}$

$8) \ \log_{5} (4x-3)>\log_{5}(3-2x)\\\\ODZ:\\\\\displaystyle\left \{ {{4x-3>0} \atop {3-2x>0}} \right. \\\\\\\displaystyle\left \{ {{x>0,75 } \atop {x<1,5}} \right. \ \Rightarrow \ x\in(0,75 \ ; \ 1,5)\\\\\\4x-3>3-2x\\\\4x+2x>3+3\\\\6x>6\\\\x>1\\\\Otvet:\boxed{x\in(1 \ ; \ 1,5)}$