Hi,

1. 5^2x-6(5^x)+5=0

 (5x)^2-6(5^x)+5=0

 let     || Good work!

 y^2-6y+5=0

factoring

(y-5)(y-1) = 0,  y = 5 0r y = 1  AND   x = 1  0r x = 1/5

As to the Remainder: the Idea is combining Like Terms...

2.4^x(5^2x)=10  ⇒ , x = 1/2 

 3.7^x+1-2=2(7^x)+3 ⇒ 7^x(7-2) = 5 ⇒ 7^x = 1,   x = 0 

 4. ⇒ 

   3^x (6*3^(-1)+1) = 3^x(2+1)= 81  ⇒  3^x = 27,    x = 3 

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