Verified answer

[tex]\displaystyle 1)(\frac{2}{3})^x*(\frac{9}{8})^x=\frac{27}{64}\\ \\(\frac{2}{3}*\frac{9}{8})^x=(\frac{3}{4})^3\\ \\(\frac{3}{4})^x=(\frac{3}{4})^3\\ \\x=3\\ \\2)\sqrt{2^x}\sqrt{3^x}=36\\ \sqrt{2^x*3^x}=6^2\\ \sqrt{(2*3)^x}=6^2\\ \sqrt{6^x}=6^2\\\\ 6^{\frac{x}{2} }=6^2 \\ \\\frac{x}{2}=2\\ \\x=4\\ \\3)\sqrt{2^x}=4\\ \\2^{\frac{x}{2} }=2^2\\ \\\frac{x}{2}=2\\ \\x=4[/tex]