Question

What is the value of x in the equation ln (x + 6) – ln (2x – 1) = 0?

Answer 1

x = 7

Explanation:

(7 + 6) - (14 - 1) = 13 - 13 = 0

Answer 2

x = 7

Explanation:

Using the rules of logarithms

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

`log_(b)` x = n ⇒ x =
`b^(n)`

Given

ln(x + 6) - ln(2x - 1) = 0

ln (
`(x+6)/(2x-1)` ) = 0

`(x+6)/(2x-1)` =
`e^(0)` = 1 , then

2x - 1 = x + 6 ( subtract x from both sides )

x - 1 = 6 ( add 1 to both sides )

x = 7