Solve for x if (25^{x} + 3(5^{x}) = 4)

A.
1 or 4 
B.
0 
C.
1 
D.
4 or 0
Correct Answer: Option B
Explanation
(25^{x} + 3(5^{x}) = 4)
Let (5^{x}) = y.
((5^{2})^{x} + 3(5^{x}) – 4 = 0)
(y^{2} + 3y – 4 = 0)
(y^{2} – y + 4y – 4 = 0)
(y(y – 1) + 4(y – 1) = 0)
((y + 4)(y – 1) = 0)
(y = 4 ; y = 1)
y = 4 is not possible.
y = 1 (implies) x = 0.