Exponential equations and inequalities

9000003708

Level: 
B
Consider the exponential equation \[ 4^{x+2} - 5\cdot 4^{x+1} + 4^{x-1} + 240 = 0 \] with \(x\in \mathbb{R}\). In the following list identify a true statement on this equation.
The equation has a unique solution. This solution is a positive integer.
The equation has a unique solution. This solution is a negative number.
The equation does not have a solution.
The equation has two solutions.
Zero is a solution of this equation.
The equation has a unique solution. This solution is a negative integer.