Question

Please help me answer this!!

Answer 1

Answer:

x = 3, x = 6

Step-by-step explanation:

Using the rules of logarithms

log x - log y = log ($\frac{x}{y}$ )

log$x^{n}$ ⇔ nlog x

$log_{b}$ x = n ⇔ x = $b^{n}$

Given

2$log_{3}$ x - $log_{3}$(x - 2) - 2 = 0 ( add 2 to both sides )

$log_{3}$ x² - $log_{3}$(x - 2) = 2

$log_{3}$ ($\frac{x^2}{x-2}$ ) = 2

$\frac{x^2}{x-2}$ = 3² = 9 ( multiply both sides by x - 2 )

x² = 9(x - 2) ← distribute

x² = 9x - 18 ( subtract 9x - 18 from both sides )

x² - 9x + 18 = 0 ← in standard form

(x - 3)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 6 = 0 ⇒ x = 6