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

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

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.

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