Question

Log(x)-log(x+6)=log(k)

Find x if k=1/2

Answer 1

x = 6

Explanation:

Using the rules of logarithms

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

logx = logy , then x = y

Given

log(x) - log(x + 6)

= log(
`(x)/(x+6)` )

Then

log )
`(x)/(x+6)` ) = log(
`(1)/(2)` ) , thus

`(x)/(x+6)` =
`(1)/(2)` ( cross- multiply )

2x = x + 6 ( subtract x from both sides )

x = 6