Question

2㏒x-㏒[x-2]=2㏒3: solve the equation

Answer 1

Step-by-step explanation:

$2 log(x) - log(x - 2) = 2 log(3)$

$log(x {}^{2} ) - log(x - 2) = log(9)$

$log( \frac{ {x}^{2} }{x - 2} ) = log(9)$

$\frac{ {x}^{2} }{x - 2} = 9$

${x}^{2} = 9x - 18$

${x}^{2} - 9x + 18 = 0$

$(x - 3)(x - 6) = 0$

$x = 3$

and

$x = 6$