Answer:
[tex] x = \frac{1}{2} \: \: or \: \: x = \frac{3}{2} [/tex]
Step-by-step explanation:
[tex]log_x(8x-3)-log_x 4= 2 \\ \\ log_x \frac{(8x - 3)}{4} = 2 \\ \\ \frac{(8x - 3)}{4} = {x}^{2} \\ \\ 8x - 3 = 4 {x}^{2} \\ \\ 4 {x}^{2} - 8x + 3 = 0 \\ \\ 4 {x}^{2} - 2x - 6x + 3 = 0 \\ \\ 2x(2x - 1) - 3(2x - 1) = 0 \\ \\ (2x - 1)(2x - 3) = 0 \\ \\ 2x - 1 = 0 \: \: or \: \: 2x - 3 = 0 \\ \\ 2x = 1 \: \: or \: \: 2x = 3 \\ \\ x = \frac{1}{2} \: \: or \: \: x = \frac{3}{2} \\ [/tex]
