Answer:
[tex] {2}^{x - 3} \times {8}^{x - 2} = \frac{1}{4} \\ {2}^{x - 3} \times {2}^{3x - 6} = \frac{1}{4} \\ {2}^{x - 3 + 3x - 6} = \frac{1}{4} \\{ 2}^{4x -9} = {2}^{ - 2} \\ log_{2}({ 2}^{4x -9}) = log_{2}({ 2}^{ - 2}) \\( 4x - 9 )log_{2}({ 2}) = ( - 2 )log_{2}({ 2})\\ 4x - 9 = - 2 \\ 4x = 7 \\ \therefore x = \frac{7}{4} [/tex]
