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