a: \(16^{-x}=8^{2\left(1-x\right)}\)
=>\(2^{-4x}=2^{6\left(1-x\right)}\)
=>6(1-x)=-4x
=>6-6x=-4x
=>-4x+6x=6
=>2x=6
=>x=6/2=3
b: \(3^{\left|3x-4\right|}=9^{2x-2}\)
=>\(3^{\left|3x-4\right|}=3^{4x-4}\)
=>\(\left|3x-4\right|=4x-4\)
=>\(\left\{{}\begin{matrix}4x-4>=0\\\left(4x-4\right)^2=\left(3x-4\right)^2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>=1\\\left(4x-4-3x+4\right)\left(4x-4+3x-4\right)=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>=1\\x\left(7x-8\right)=0\end{matrix}\right.\)
=>\(x=\dfrac{8}{7}\)
c: \(32^{\dfrac{x+5}{x-4}}=0,25\cdot128^{\dfrac{x+17}{x-3}}\)
=>\(2^{\dfrac{5x+25}{x-4}}=2^{-2}\cdot2^{\dfrac{7x+119}{x-3}}\)
=>\(\dfrac{5x+25}{x-4}=-2+\dfrac{7x+119}{x-3}\)
=>\(\dfrac{5x+25}{x-4}=\dfrac{-2x+6+7x+119}{x-3}\)
=>\(\dfrac{5x+25}{x-4}=\dfrac{5x+125}{x-3}\)
=>\(\left(5x+25\right)\left(x-3\right)=\left(5x+125\right)\left(x-4\right)\)
=>\(\left(x+5\right)\left(x-3\right)=\left(x+25\right)\left(x-4\right)\)
=>\(x^2-3x+5x-15=x^2-4x+25x-100\)
=>2x-15=21x-100
=>2x-21x=-100+15
=>-19x=-85
=>\(x=\dfrac{85}{19}\)
