a. -28√10 b. 28√10 c. 24√14 d. 40√14

[tex]\displaystyle 6^{4\log x}\cdot3^{-3\log x}=48\\2^{4\log x}\cdot3^{4\log x}\cdot3^{-3\log x}=48\\2^{4\log x}\cdot3^{4\log x-3\log x}=48\\2^{4\log x}\cdot3^{\log x}=16\cdot3\\\therefore\\\log x=1\\x=10[/tex]

[tex]\displaystyle \lim_{p\to10}\frac{2p^2-20p}{\sqrt{2p-6}-\sqrt{p+4}}=\lim_{p\to10}\frac{(2p^2-20p)(\sqrt{2p-6}+\sqrt{p+4})}{2p-6-p-4}\\\lim_{p\to10}\frac{2p^2-20p}{\sqrt{2p-6}-\sqrt{p+4}}=\lim_{p\to10}\frac{2p(p-10)(\sqrt{2p-6}+\sqrt{p+4})}{p-10}\\\lim_{p\to10}\frac{2p^2-20p}{\sqrt{2p-6}-\sqrt{p+4}}=\lim_{p\to10}2p(\sqrt{2p-6}+\sqrt{p+4})\\\lim_{p\to10}\frac{2p^2-20p}{\sqrt{2p-6}-\sqrt{p+4}}=2(10)(\sqrt{2(10)-6}+\sqrt{10+4})\\\boxed{\boxed{\lim_{p\to10}\frac{2p^2-20p}{\sqrt{2p-6}-\sqrt{p+4}}=40\sqrt{14}}}[/tex]