\(a,4^{x-2}+4^{x+1}=1040\\ =>4^{x-2}\cdot\left(1+4^3\right)=1040\\ =>4^{x-2}\cdot65=1040\\ =>4^{x-2}=1040:65\\ =>4^{x-2}=26=4^2\\ =>x-2=2\\ =>x=2+2=4\\ b,\left(2x-1\right)^3=-8\\ =>\left(2x-1\right)^3=\left(-2\right)^3\\ =>2x-1=-2\\ =>2x-1=-2+1\\ =>2x=-1\\ =>x=-\dfrac{1}{2}\\ c,\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\\ =>\left(x-1\right)^{x+4}-\left(x-1\right)^{x+2}=0\\ =>\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\\ TH1:\left(x-1\right)^{x+2}=0\\ =>x-1=0\\ =>x=1\\ TH2:\left(x-1\right)^2=1\\ +)x-1=1\\ =>x=2\\ +)x-1=-1\\ =>x=0\\ d,2^{x+1}\cdot3^y=12^x\\ =>2^{x+1}\cdot3^y=2^{2x}\cdot3^x\\ =>\dfrac{2^{x+1}\cdot3^y}{2^{2x}\cdot3^x}=1\\ =>2^{1-x}\cdot3^{y-x}=1\\ =>\left[{}\begin{matrix}1-x=0\\y-x=0\end{matrix}\right.\\ =>x=y=1\)
