Question

Ln x - ln 2 = ln 3- ln (x+1) find the value of x

Answer 1

x = 2

Explanation:

using the properties of logarithms

• logx - logy = log (
`(x)/(y)` )

• loga = log b ⇒ a = b

given

ln x - ln 2 = ln 3 - ln(x + 1)

ln (
`(x)/(2)` ) = ln(
`(3)/(x+1)` )

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

x(x + 1) = 6

x² + x = 6 ( subtract 6 from both sides )

x² + x - 6 = 0 ← in standard form

(x + 3)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = 0 3

x - 2 = 0 ⇒ x = 2

but x > 0 , then x = 2