a: \(81^{\frac{x+10}{x-10}}=\left(\frac{1}{27}\right)\cdot27^{\frac{x+5}{x-15}}\)
=>\(\left(3^4\right)^{\frac{x+10}{x-10}}=3^{-3}\cdot\left(3^3\right)^{\frac{x+5}{x-15}}\)
=>\(\frac{4\left(x+10\right)}{x-10}=-3+\frac{3\left(x+5\right)}{x-15}=\frac{-3\left(x-15\right)+3\left(x+5\right)}{x-15}\)
=>\(\frac{4x+40}{x-10}=\frac{-3x+45+3x+15}{x-15}=\frac{60}{x-15}\)
=>\(\frac{x+10}{x-10}=\frac{15}{x-15}\)
=>(x+10)(x-15)=15(x-10)
=>\(x^2-5x-150=15x-150\)
=>\(x^2-20x=0\)
=>x(x-20)=0
=>x=0 hoặc x=20
b: \(9\cdot2^{2x}=8\cdot\sqrt{3^{2x+1}}\)
=>\(3^2\cdot2^{2x}=2^3\cdot3^{\frac12\left(2x+1\right)}=2^3\cdot3^{x+\frac12}\)
=>\(\frac{2^{2x}}{2^3}=\frac{3^{x+\frac12}}{3^2}\)
=>\(2^{2x-3}=3^{x+\frac12-2}=3^{x-\frac32}\)
=>2x-3=0
=>x=3/2
