Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises - Page 527: 44

$x = 1, 2 $

$(\frac{1}{4})^{x^{2} - 3x} = 16$ $(4^{-1})^{x^{2} - 3x} = 4^{2}$ $4^{-x^{2} + 3x} = 4^{2}$ $-x^{2} + 3x = 2$ $-x^{2} + 3x - 2 = 0$ $-x^{2} + 2x + x - 2 = 0$ $-x(x - 2) + 1(x-2) = 0$ $(-x + 1)(x-2) = 0$ $-x + 1 = 0$ $-x = -1$ $x = 1$ $x -2 = 0$ $x = 2$ $x = 1, 2 $