Question

What is the solution to this equation?

Answer 1

D

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

`log_(3)` (4x) - 2
`log_(3)` x = 2

`log_(3)` (4x) -
`log_(3)` x² = 2

`log_(3)` (
`(4x)/(x^2)` ) = 2

`log_(3)` (
`(4)/(x)` ) = 2

`(4)/(x)` = 3² = 9 ( multiply both sides by x )

4 = 9x ( divide both sides by 9 )

`(4)/(9)` = x → D