Answer:
x = - 1, 4
Step-by-step explanation:
[tex]log(x - 1) + log(x - 2) = log \: 2 + log \: 3 \\ \\ log \{(x - 1) (x - 2) \} = log \{2 \times 3 \}\\ \\ log \{ {x}^{2} - 2x - x + 2 \} = log \:6\\ \\ {x}^{2} - 3x+ 2 = 6 \\ \\ {x}^{2} - 3x+ 2 - 6 = 0\\ \\ {x}^{2} - 3x - 4 = 0\\ \\ {x}^{2} - 4x + x - 4 = 0\\ \\ x(x - 4) + 1(x - 4) = 0 \\ \\ (x - 4)(x + 1) = 0 \\ \\ x - 4 = 0 \: \: or \: \: x + 1 = 0 \\ \\ x = 4 \: \: or \: \: x = - 1 \\ \\ x = - 1, \: \: 4[/tex]
