1. 5^2x(1/5-1)+2^2x(1+4)=0
-4/5*5^2x+5*2^2x=0 |*5
-(2*5^x)^2+(5*2^x)^2=0
(5*2^x-2*5^x)*(5*2^x+2*5^x)=0
5*2^x=2*5^x
2^{x-1}=5^{x-1}
x-1=0
x=1
(5*2^x+2*5^x)=0
5*2^x=-2*5^x
2^{x-1}=-5^{x-1} not decision
.b)
4^x-10*2^{x-1}-24=0
(2^x)^2-2*(2^x)5/2+25/4 - (96+25)/4=0
((2^x)-5/2)^2-(11/2)^2=0
((2^x)-5/2-11/2)*((2^x)-5/2+11/2)=0
(2^x)-16/2=0 (2^x)+6/2=0
(2^x)=8 (2^x)=-3 not decision
x=3
2.
2^x+2^y=12
x-y=1
x=1+y
2^y(2+1)=12
2^y=4
y=2
x=3