Step-by-step Solution:

Mode = 3.Median – 2.Mean \[ 9^x = 3 \times 3^x - 2 \] Rewriting \(9^x\) as \((3^x)^2\): \[ (3^x)^2 = 3 \times 3^x - 2 \] Let \( y = 3^x \). Then the equation becomes: \[ y^2 = 3y - 2 \] Rearranging: \[ y^2 - 3y + 2 = 0 \] Factoring the quadratic equation: \[ (y - 1)(y - 2) = 0 \] Thus, \(y = 1\) or \(y = 2\). Since \(y = 3^x\). \[\] we now solve for \(x\): \[\] When \(y = 1\), \(3^x = 1\), so \(x = 0\). \[\] When \(y = 2\), \(3^x = 2\), so \(x = \log_3 2\). Now, we calculate the values of \(9^x\): \[\] When \(x = 0\), \(9^x = 1\). \[\] When \(x = \log_3 2\), \(9^x = 4\). \[\] So, the possible values for the mode are \(1\) and \(4\).