Question

me dá uma ajudinha aê galera, AGRADEÇO
$a) log_{2}(x-1)<log_{2}3$
$b) log_ \frac{1}{3}x \leq log_ \frac{1}{3}2$
$c) log x_{3}(2x-7) >log_{3}5$
$d) log_{0,3}x \leq log_{0,3}(-x+3)$
$e) log_{4}(3x-2)>log_{4}(5x-1)$

Answer 1

$a) \\ log_2(x-1)2\\ \\ c) \\ log_3(2x-7)>log_35\rightarrow 2x-7>5 \rightarrow 2x>12\rightarrow x>6\\ \\ d) \\ log_{0,3}x \leq log_{0,3}(-x+3) \rightarrow x>-x+3\rightarrow 2x>3\rightarrow x>\frac{3}{2}\\ \\ e) \\ log_4(3x-2)>log_4(5x-1) \rightarrow 3x-2>5x-1\\ \\ 3x-5x>-1+2\\ \\ -2x>1\\ \\ x<\frac{1}{2}$