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

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.