[tex]\it a)\ (5^2)^x=5^{23}\cdot5^{13} \Rightarrow 5^{2x}=5^{36} \Rightarrow 2x=36 \Rightarrow x=36:2 \Rightarrow x=18\\ \\ b)\ \dfrac{3}{5}\geq\dfrac{x+1}{35}\geq\dfrac{3}{7}|_{\cdot{35}} \Rightarrow 21\geq x+1\geq15|_{-1} \Rightarrow 20\geq x\geq14 \Rightarrow \\ \\ \\ \Rightarrow 14\leq x\leq20 \Rightarrow x\in\{14,\ 15,\ 16,\ 17,\ 18,\ 19,\ 20\}[/tex]
