Math help please?

Question

Solve this equation for x: ln (x + 1) - ln x = 2

Answer 1

The equation is ln(x + 1) - ln x = 2.

Apply quotient property logarithm:

ln[(x + 1)/x] = 2

Apply basic principle of logarithm : log_ex = y ⇔ x = e^y .

(x + 1)/x = e²

(x + 1)/x = 7.389

x + 1 = 7.389x

1 = 7.389x - x

1 = x(7.389 - 1)

x(6.389) = 1

x = 1/6.389

⇒ x = 0.1565.

The solution is x = 0.1565.