if logx (8x-3) -logx 4=2, the value of x is

Answer: x = 1/2 and 3/2 Step-by-step explanation:The given equation is logₓ (8x-3) - logₓ 4 = 2Then we have to determine the value of x.logₓ [tex][\frac{(8x-3)}{4}][/tex] = 2    [ since log a - log b = log [tex](\frac{a}{b})[/tex] ]Now [tex]x^{2}=\frac{(8x-3)}{4}[/tex]   [if [tex]log_{a}[/tex]b = c then [tex]a^{c}[/tex] = b]4x² = 8x -3 4x² - 8x + 3 = 0(2x)² - 2(4x) + (4-4) + 3 = 0[(2x)² - 2 (4x) + 4 ] - 1 = 0(2x - 2)² = 1(2x - 2)² = ± 1 ⇒ 2x - 2 = 1       and      2x - 2 = -1x = 3/2                        2x = 1                                     x = 1/2Therefore, x = 1/2 and 3/2 are the answers.