Question

What is the solution to log2 (9x)- log2^3=3?

x=3/8. x=8/3
x=3
X=9

Answer 1

x =
`(8)/(3)`

Explanation:

Using the rule of logarithms

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

`log_(b)` x = n ⇒ x =
`b^(n)`

Given

`log_(2)` (9x) -
`log_(2)` 3 = 3

`log_(2)` (
`(9x)/(3)` ) = 3

`log_(2)` 3x = 3

3x = 2³ = 8 ( divide both sides by 3 )

x =
`(8)/(3)`