Question

If log x (8x-3) -log x 4=2 , the value of x is

Answer 1

`x = (1)/(2) \: \: or \: \: x = (3)/(2)`

Explanation:

`log_x(8x-3)-log_x 4= 2 \\ \\ log_x ((8x - 3))/(4) = 2 \\ \\ ((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 = (1)/(2) \: \: or \: \: x = (3)/(2) \\`