Question

Please help me answer this!!

Answer 1

x = 3, x = 6

Explanation:

Using the rules of logarithms

log x - log y = log (
`(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)` (
`(x^2)/(x-2)` ) = 2

`(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