Question

Solve: ㏒₃x² - ㏒₃(x+6)=1

Answer 1

Step-by-step explanation:

We have,

$log_{3}( {x}^{2} ) - log_{3}(x + 6) = 1$

$= > log_{3}( \frac{ {x}^{2} }{x + 6}) = 1$

$= > \frac{ {x}^{2} }{x + 6} = 3$

$= > {x}^{2} = 3x + 18$

$= > {x}^{2} - 3x - 18 = 0$

$= > {x}^{2} - 6x + 3x - 18 = 0$

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

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

$= > x = 6 \: \: or \: \: x = - 3$