Question

Log k-log(k-2)=log25

Answer 1

k =
`(25)/(12)`

Explanation:

Using the rules of logarithms

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

log a = log b ⇒ a = b

Given

logk - log(k - 2) = log25, then

log (
`(k)/(k-2)` ) = log25, thus

`(k)/(k-2)` = 25 ( multiply both sides by (k - 2)

25(k - 2) = k

25k - 50 = k ( subtract k from both sides )

24k - 50 = 0 ( add 50 to both sides )

24k = 50 ( divide both sides by 24 )

k =
`(50)/(24)` =
`(25)/(12)`